Systems and Methods for Quantum Computing

Abstract

The present disclosure describes non-classical (e.g., quantum) computing systems and methods that utilize dopant molecules contained in a host material as qubits. The dopant molecules generally include triplet ground state (GST) molecules such as carbenes or nitrenes. The host material generally includes organic molecules. Precursors to the dopant molecules are embedded in the host material and then subjected to ultraviolet (UV) or visible light to form a dilute molecular crystal containing the dopant molecules embedded in the host material. The triplet sub-levels of the dopant molecules can be manipulated using electromagnetic (EM) radiation such as optical, radio frequency (RF), and / or microwave (MW) radiation to perform non-classical computing operations.

Description

Technical Field

[0001] Cross - Reference to Related Applications This application claims priority to U.S. Provisional Patent Application No. 63 / 364,540, filed May 11, 2022, and U.S. Provisional Patent Application No. 63 / 379,905, filed October 18, 2022, each of which is hereby incorporated by reference in its entirety for all purposes.

[0002] The disclosed embodiments generally relate to non - classical (e.g., quantum) computing systems and methods that utilize dopant molecules contained in a host material as qubits.

Background Art

[0003] Non-classical computers (e.g., quantum computers) typically utilize quantum mechanical phenomena such as superposition, entanglement, and interference to perform data computing operations. Compared to classical computers that utilize binary numbers (bits) that always have a defined state (0 or 1), non-classical computers utilize quantum bits (qubits) that can exist in a superposition of basis states (i.e., some linear combination of the basis states |0> and |1>, where the basis states |0> and |1> are orthonormal). The various qubits of a non-classical computer may be entangled with other qubits (i.e., the quantum states of two or more qubits may be correlated such that an operation on one qubit affects the state of the entangled qubits). Quantum operations can be performed to probabilistically converge the state of the qubits to a particular final state that represents a solution to some problem. For certain classes of problems, non-classical computers can converge to a solution faster than would be possible using any known algorithm on a classical computer. In some cases, this “quantum advantage” can enable non-classical computers to solve problems that would be intractable for any known classical computer to handle. Such problems include factoring large relatively prime numbers (e.g., to break modern cryptographic hash functions), searching for a particular item within a large amount of data, and simulating the chemical behavior of drugs, materials, or other molecules. SUMMARY OF THE INVENTION

[0004] In some embodiments, the present disclosure describes non-classical (e.g., quantum) computing systems and methods that utilize dopant molecules contained within a host material as qubits.

[0005] It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosed embodiments as claimed. BRIEF DESCRIPTION OF THE DRAWINGS

[0006] The accompanying drawings, which include some portions of this specification, illustrate several embodiments and, together with the specification, serve to explain the particular principles and features of the disclosed embodiments. In the drawings,

[0007]

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DETAILED DESCRIPTION OF THE INVENTION

[0008] Here, exemplary embodiments will be described in detail and discussed with reference to the accompanying drawings. Unless otherwise defined, technical and / or scientific terms have the meanings commonly understood by one of ordinary skill in the art. The disclosed embodiments are described in sufficient detail to enable one of ordinary skill in the art to practice the disclosed embodiments. Of course, other embodiments may be utilized and changes may be made without departing from the scope of the disclosed embodiments. Accordingly, the materials, methods, and examples are illustrative only and are not intended to be limiting.

[0009] As used herein, the term "or" is intended to convey both disjunctive and conjunctive meanings as long as such a meaning is possible. For example, the phrase "A or B" is to be interpreted to include only element A, only element B, and the combination of elements A and B as long as such a meaning is possible. As another example, the phrase "A, B, or C" is to be interpreted to include only element A, only element B, only element C, the combination of elements A and B (without element C), the combination of elements A and C (without element B), the combination of elements B and C (without element A), and the combination of elements A, B, and C as long as such a meaning is possible.

[0010] In the figures (also "FIGs." or "Figs."), like numerals refer to like elements.

[0011] Non-classical computers (e.g., quantum computers) typically utilize quantum mechanical phenomena such as superposition, entanglement, and interference to perform computational operations on data. Compared to classical computers that utilize binary numbers (bits) which always have a defined state (0 or 1), non-classical computers utilize quantum bits (qubits) that can exist in a superposition of basis states (i.e., some linear combination of the basis states |0> and |1>). The various qubits of a non-classical computer may be entangled with other qubits (i.e., the quantum states of two or more qubits can be correlated such that an operation on one qubit affects the state of the entangled qubit). Quantum operations can be performed to probabilistically converge the state of the qubits to a solution to some problem. For certain classes of problems, non-classical computers can converge to a solution faster than is possible using any known algorithm on a classical computer. In some cases, this “quantum advantage” can enable non-classical computers to solve problems that would be intractable for any known classical computer to handle. Such problems include factoring large relatively prime numbers (e.g., to break modern cryptographic hash functions), searching for specific items within large amounts of data, and simulating the chemical behavior of drugs, materials, or other molecules.

[0012] Numerous chemical and physical systems have been proposed for use as qubits in non-classical computers. For example, a significant amount of resources have been directed towards superconducting qubits that utilize Josephson junctions (i.e., superconductor-insulator-superconductor transitions). Such superconducting qubits utilize different quantum tunneling modes through the Josephson junction as the ground state. These superconducting qubits can be fabricated using well-known semiconductor manufacturing techniques, enabling relatively simple circuit designs. However, superconducting qubits suffer from several drawbacks. For example, superconducting qubits generally must be cooled to just a few degrees above absolute zero and require complex cryogenic systems. Such use of complex cryogenics also makes it difficult to scale beyond a few qubits and limits the ultimate computational power of superconducting qubit-based non-classical computers.

[0013] A number of other systems, including trapped ion arrays, trapped neutral atom arrays, and chemical defects in solid lattices, have been used as qubits. One system proposed for use in quantum computing is the so-called nitrogen-vacancy (NV) center in diamond. The electron spin associated with the NV center can be optically initialized, and its spin state can be read out by fluorescence detection. Furthermore, the electron spin can be manipulated by microwave (MW) or radio frequency (RF) irradiation and can exhibit relatively long relaxation times and coherence times. However, existing NV quantum computers can support only a limited number of qubits before the adverse effects associated with an increase in the number of qubits lead to a decrease in the relaxation time and coherence time, negating the very properties that make NV quantum computers attractive in the first place. This is due to the fact that the natural abundance of carbon-13 ( 13 C) spins in diamond is 1.1%. Increasing the isotope concentration of 13 C spins in diamond increases the number of nearby 13 C spins, resulting in worse NV center properties. Furthermore, 13The random distribution of C spins results in coupling on a very wide scale, and some 13 C spins are very strongly coupled to the NV centers (e.g., in the case of adjacent 13 C spins). This can make it difficult to manipulate and control the NV centers. Furthermore, all NV centers 13 due to the random distribution of C spins, have different associated 13 C spin baths, so the NV qubits interact almost exclusively with a single NV spin, resulting in a low signal-to-noise (SNR) and requiring multiple executions of non-classical calculations to achieve a measurable signal. Additionally, it can be difficult to prepare highly crystalline diamonds with a controlled NV doping rate, so it can be difficult to prepare diamonds doped controllably at NV centers.

[0014] Accordingly, there is a need for qubits based on chemical or physical systems that avoid problems associated with known qubits. Ideally, such chemical or physical systems should be relatively simple to fabricate on a single device, support hundreds or thousands of qubits, allow each qubit to be operated independently from all other qubits, and have a coherence lifetime that is substantially longer than the time required to perform a quantum operation on each qubit. Systems consistent with the disclosed embodiments can meet some or all of these criteria and thus can provide a technological improvement in the implementation of non-classical computing.

[0015] As used herein, the terms "non-classical computing," "non-classical procedure," "non-classical operation," and "non-classical computer" generally refer to any system or method for performing a computational procedure outside of the paradigm of classical computing. Non-classical computing, non-classical procedures, non-classical operations, or non-classical computers may include quantum computing, quantum procedures, quantum operations, or quantum computers.

[0016] As used herein, the terms "quantum computing," "quantum procedure," "quantum operation," and "quantum computer" generally refer to any method or system for performing calculations using quantum mechanical operations (such as unitary transformations or completely positive trace-preserving (CPTP) maps on a quantum channel) represented by a quantum device on a Hilbert space. Thus, quantum and classical (or digital) computing can be similar in the following aspects. That is, both types of computing may include a sequence of instructions that are performed on input information and then provide an output. Various paradigms of quantum computing can decompose a quantum operation into a sequence of basic quantum operations that simultaneously affect a subset of the qubits of a quantum device. The quantum operations can be selected, for example, based on their locality or ease of physical implementation. A quantum procedure or calculation can then consist of a sequence of instructions that can represent different quantum evolutions on a quantum device for various applications. For example, a procedure for calculating or simulating quantum chemistry can represent quantum states, as well as annihilation and creation operators of electron spin orbitals, by using qubits (such as two-level quantum systems) and a universal set of quantum gates (such as Hadamard, controlled Not (CNOT), and π / 8 rotations) via so-called Jordan-Wigner transformation or Bravyi-Kitaev transformation.

[0017] Further examples of quantum procedures or calculations can include procedures for optimization such as the quantum approximate optimization algorithm (QAOA) or quantum minimum finding. QAOA can include performing rotations of single qubits and entangling gates of multiple qubits. In quantum adiabatic computing, the instructions may carry the initial quantum system along a probabilistic or non-probabilistic path of evolution to a final one. Quantum-inspired procedures can include simulated annealing, parallel tempering, master equation solvers, Monte Carlo procedures, quantum algorithms for approximating the maximum independent set, and the like. Quantum-classical or hybrid algorithms or procedures can include procedures such as the variational quantum eigenvalue solver (VQE), as well as the variational and adiabatically navigated quantum eigenvalue solver (VanQver).

[0018] Generally, an example of a quantum procedure or computation may include any procedure or computation described in M.A. Nielsen and I.L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press (2013), which is hereby incorporated by reference in its entirety for all purposes.

[0019] A quantum computer may comprise one or more adiabatic quantum computers, quantum gate arrays, one-way quantum computers, topological quantum computers, quantum Turing machines, quantum annealers, Ising solvers, or gate models of quantum computation.

[0020] A host material doped as a qubit for performing non-classical computations Provided herein are systems and methods for performing non-classical computations. The systems and methods generally utilize dopant molecules contained within an organic host material. The dopant molecules generally function as qubits and are associated with an electronic energy level structure that includes a triplet electron manifold. The triplet electron manifold may include a ground state triplet (GST) electron manifold. The triplet electron manifold generally includes three triplet states, which may be linearly combined to form the ground state of a qubit (e.g., with respect to a laboratory reference frame, a rotating reference frame, or another suitable time-independent or time-dependent reference frame). The ground state generally has a long lifetime at a temperature that can be obtained using a liquid helium-based cryogenic system. The dopant molecules are arranged within the host material to enable a relatively strong coupling between neighboring dopant molecules and to enable the spread of information across the entangled qubit network. The quantum states of the various dopant molecules may be individually manipulated using optical, MW, or RF techniques, enabling individual control of each qubit for performing non-classical computations.

[0021] FIG. 1A shows a top view of a system 100 for performing non-classical computing according to various embodiments. In the illustrated example, system 100 includes at least one host material 110. In some embodiments, host material 110 includes at least one organic molecule. In some embodiments, host material 110 is referred to herein as a "matrix".

[0022] In some embodiments, host material 110 includes a crystalline host material. In some embodiments, host material 110 includes a single-crystalline host material. In some embodiments, host material 110 includes a polycrystalline host material. In some embodiments, host material 110 includes a liquid-crystalline host material. In some embodiments, host material 110 includes an amorphous host material. In some embodiments, host material 110 includes a powdered host material. In some embodiments, host material 110 includes a frozen-solution host material. In some embodiments, a frozen-solution host material includes a solution frozen at cryogenic temperatures. For example, in some embodiments, a frozen-solution host material is frozen at a temperature of at least about 1 kelvin (K), 2K, 3K, 4K, 5K, 6K, 7K, 8K, 9K, 10K, 15K, 20K, 25K, 30K, 35K, 40K, 45K, 50K, or more, up to about 50K, 45K, 40K, 35K, 30K, 25K, 20K, 15K, 10K, 9K, 8K, 7K, 6K, 5K, 4K, 3K, 2K, 1K, or less, or at a temperature between any two of the foregoing values.

[0023] In some embodiments, the host material 110 includes a linear or branched alkane. In some embodiments, the linear or branched alkane includes a C4-C20 linear or branched alkane. In some embodiments, the linear or branched alkane includes a C4 linear or branched alkane, a C5 linear or branched alkane, a C6 linear or branched alkane, a C7 linear or branched alkane, a C8 linear or branched alkane, a C9 linear or branched alkane, a C10 linear or branched alkane, a C11 linear or branched alkane, a C12 linear or branched alkane, a C13 linear or branched alkane, a C14 linear or branched alkane, a C15 linear or branched alkane, a C16 linear or branched alkane, a C17 linear or branched alkane, a C18 linear or branched alkane, a C19 linear or branched alkane, or a C20 linear or branched alkane. In some embodiments, the host material 110 includes an aromatic hydrocarbon. In some embodiments, the host material 110 includes a polyaromatic hydrocarbon. In some embodiments, the polyaromatic hydrocarbon is optionally substituted with a methylene, nitrile, carbonyl, carboxylate, alkyl, deuterated alkyl, aryl, deuterated aryl, heteroaryl, deuterated heteroaryl, borane, imine, amine, nitro, phosphine, thioether, ether, fluoro, chloro, bromo, iodo, or thiocarbonyl group. In some embodiments, the host material 110 includes a diaryl ketone. In some embodiments, the host material 110 includes octasulfur. In some embodiments, the host material 110 includes naphthalene, anthracene, para-terphenyl, benzoic acid, fluorene, biphenyl, benzene, n-hexane, biphenylene, ortho-terphenylen, meta-terphenylen, para-terphenylen, di(phenyl)methanone, phenanthrene, or di(naphthalen-2-yl)methanone. In some embodiments, the host material 110 includes any of the foregoing optionally partially or fully isotopically labeled derivatives.

[0024] In some embodiments, host material 110 is at least partially deuterated. That is, in some embodiments, host material 110 contains one or more deuterium atoms where a hydrogen atom would otherwise be expected. In some embodiments, host material 110 contains at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, or more deuterium atoms, up to about 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 deuterium atom, or a number of deuterium atoms within a range defined by any two of the foregoing values. In some embodiments, host material 110 is fully deuterated. That is, in some embodiments, host material 110 contains deuterium atoms at all sites where a hydrogen atom would otherwise be expected. In some embodiments, host material 110 is at least partially labeled with carbon-13. That is, in some embodiments, host material 110 contains one or more carbon-13 atoms where a carbon-12 atom would otherwise be expected. In some embodiments, host material 110 contains at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, or more carbon-13 atoms, up to about 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 carbon-13 atom, or a number of carbon-13 atoms within a range defined by any two of the foregoing values.

[0025] In some embodiments, host material 110 comprises an isotopically enriched host material. In some embodiments, host material 110 is isotopically enriched with a particular atomic isotope. In some embodiments, the isotope is hydrogen ( 1 H), deuterium ( 2 H), carbon-13 ( 13 C), nitrogen-15 ( 15 N), fluorine-19 ( 19F), silicon-29 ( 29 Si), or phosphorus-31 ( 31 P). In some embodiments, the host material 110 is at least about 1%, 2%, 3%, 4%, 5%, 6%, 7%, 8%, 9%, 10%, 15%, 20%, 25%, 30%, 35%, 40%, 45%, 50%, 55%, 60%, 65%, 70%, 75%, 80%, 85%, 90%, 91%, 92%, 93%, 94%, 95%, 96%, 97%, 98%, 99%, or more, up to about 99%, 98%, 97%, 96%, 95%, 94%, 93%, 92%, 91%, 90%, 85%, 80%, 75%, 70%, 65%, 60%, 55%, 50%, 45%, 40%, 35%, 30%, 25%, 20%, 15%, 10%, 9%, 8%, 7%, 6%, 5%, 4%, 3%, 2%, 1%, or less in abundance, or is isotope enriched to have an abundance within a range defined by any two of the foregoing values so as to characterize the isotope. In some embodiments, the isotope enrichment enables improved control over the magnetic environment of the dopant molecule 120 described herein.

[0026] In some embodiments, the host material 110 does not include diamond or graphite.

[0027] In some embodiments, the host material 110 is configured to contain at least one dopant molecule 120 described herein.

[0028] In the illustrated embodiment, the system 100 includes a plurality of dopant molecules 120. In some embodiments, the plurality of dopant molecules 120 are contained in the host material 110. In some embodiments, each dopant molecule 120 includes a qubit for use in performing non - classical calculations. The quantum state of the qubit is described in more detail in FIG. 2.

[0029] In some embodiments, each dopant molecule 120 includes an organic molecule. In some embodiments, each dopant molecule 120 includes a GST molecule, i.e., in some embodiments, each dopant molecule 120 is associated with the GST electronic manifold as described herein with respect to FIG. 2.

[0030] In some embodiments, at least one dopant molecule 120 includes a carbene molecule. In some embodiments, at least one dopant molecule 120 includes a nitrene molecule. In some embodiments, at least one dopant molecule 120 includes a biradical molecule. In some embodiments, at least one dopant molecule 120 includes a diradical molecule. In some embodiments, at least one dopant molecule 120 includes a diaryldiazomethane compound, di(naphthalen-2-yl)carbene, or diphenylcarbene. In some embodiments, at least one dopant molecule 120 includes any partial or fully isotopically labeled derivative of any of the foregoing.

[0031] In some embodiments, at least one dopant molecule 120 is at least partially deuterated. That is, in some embodiments, at least one dopant molecule 120 contains one or more deuterium atoms where a hydrogen atom would otherwise be expected. In some embodiments, at least one dopant molecule 120 contains at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, or more deuterium atoms, up to about 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 deuterium atom, or a number of deuterium atoms within a range defined by any two of the foregoing values. In some embodiments, at least one dopant molecule 120 is fully deuterated. That is, in some embodiments, at least one dopant molecule 120 contains deuterium atoms at all sites where a hydrogen atom would otherwise be expected. In some embodiments, at least one dopant molecule 120 is at least partially labeled with carbon-13. That is, in some embodiments, at least one dopant molecule 120 contains one or more carbon-13 atoms where a carbon-12 atom would otherwise be expected. In some embodiments, at least one dopant molecule 120 contains at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, or more carbon-13 atoms, up to about 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 carbon-13 atom, or a number of carbon-13 atoms within a range defined by any two of the foregoing values.

[0032] In some embodiments, at least one dopant molecule 120 is bound to at least one other dopant molecule 120 by a binding interaction 130. In some embodiments, at least one dopant molecule 120 is bound by a binding interaction 130 to at least about 1, 2, 3, 4, 5, 6, 7, 8, or more other dopant molecules 120, up to about 8, 7, 6, 5, 4, 3, 2, or 1 other dopant molecule 120, or a number of dopant molecules within a range defined by any two of the foregoing values. For example, in some embodiments, at least one dopant molecule 120 is bound to about 1 to about 2, about 1 to about 3, about 1 to about 4, about 1 to about 5, about 1 to about 6, about 1 to about 7, about 1 to about 8, about 2 to about 3, about 2 to about 4, about 2 to about 5, about 2 to about 6, about 2 to about 7, about 2 to about 8, about 3 to about 4, about 3 to about 5, about 3 to about 6, about 3 to about 7, about 3 to about 8, about 4 to about 5, about 4 to about 6, about 4 to about 7, about 4 to about 8, about 5 to about 6, about 5 to about 7, about 5 to about 8, about 6 to about 7, about 6 to about 8, or about 7 to about 8 other dopant molecules 120.

[0033] In some embodiments, each dopant molecule is bound to at least one other dopant molecule by a binding interaction 130. In some embodiments, each dopant molecule 120 is bound by a binding interaction 130 to at least about 1, 2, 3, 4, 5, 6, 7, 8, or more other dopant molecules 120, up to about 8, 7, 6, 5, 4, 3, 2, or 1 other dopant molecule 120, or a number of dopant molecules within a range defined by any two of the foregoing values. For example, in some embodiments, each dopant molecule 120 is bound to about 1 to about 2, about 1 to about 3, about 1 to about 4, about 1 to about 5, about 1 to about 6, about 1 to about 7, about 1 to about 8, about 2 to about 3, about 2 to about 4, about 2 to about 5, about 2 to about 6, about 2 to about 7, about 2 to about 8, about 3 to about 4, about 3 to about 5, about 3 to about 6, about 3 to about 7, about 3 to about 8, about 4 to about 5, about 4 to about 6, about 4 to about 7, about 4 to about 8, about 5 to about 6, about 5 to about 7, about 5 to about 8, about 6 to about 7, about 6 to about 8, or about 7 to about 8 other dopant molecules 120. In some embodiments, the set of dopant molecules 120 to which each dopant molecule 120 is bound is referred to as its "nearest neighbors."

[0034] In some embodiments, the binding interaction 130 includes an electronic binding interaction. In some embodiments, the binding interaction 130 includes an electron dipole binding interaction. In some embodiments, the binding interaction 130 includes a magnetic binding interaction. In some embodiments, the binding interaction 130 has a binding strength. In some embodiments, the binding strength is at least about 100 Hertz (Hz), 200 Hz, 300 Hz, 400 Hz, 500 Hz, 600 Hz, 700 Hz, 800 Hz, 900 Hz, 1 kilohertz (kHz), 2 kHz, 3 kHz, 4 kHz, 5 kHz, 6 kHz, 7 kHz, 8 kHz, 9 kHz, 10 kHz, 20 kHz, 30 kHz, 40 kHz, 50 kHz, 60 kHz, 70 kHz, 80 kHz, 90 kHz, 100 kHz, 200 kHz, 300 kHz, 400 kHz, 500 kHz, 600 kHz, 700 kHz, 800 kHz, 900 kHz, 1 megahertz (MHz), 2 MHz, 3 MHz, 4 MHz, 5 MHz, 6 MHz, 7 MHz, 8 MHz, 9 MHz, 10 MHz, or more, up to about 10 MHz, 9 MHz, 8 MHz, 7 MHz, 6 MHz, 5 MHz, 4 MHz, 3 MHz, 2 MHz, 1 MHz, 900 kHz, 800 kHz, 700 kHz, 600 kHz, 500 kHz, 400 kHz, 300 kHz, 200 kHz, 100 kHz, 90 kHz, 80 kHz, 70 kHz, 60 kHz, 50 kHz, 40 kHz, 30 kHz, 20 kHz, 10 kHz, 9 kHz, 8 kHz, 7 kHz, 6 kHz, 5 kHz, 4 kHz, 3 kHz, 2 kHz, 1 kHz, 900 Hz, 800 Hz, 700 Hz, 600 Hz, 500 Hz, 400 Hz, 300 Hz, 200 Hz, 100 Hz, or less, or within a range defined by any two of the foregoing values. For example, in some embodiments, the binding strength is from about 100 Hz to about 1,000 kHz, from about 100 Hz to about 100 kHz, from about 100 Hz to about 10 kHz, from about 100 Hz to about 1 kHz, from about 1 kHz to about 1,000 kHz, from about 1 kHz to about 100 kHz, from about 1 kHz to about 10 kHz, from about 10 kHz to about 1,000 kHz, from about 10 kHz to about 100 kHz, or from about 100 kHz to about 1,000 kHz. In some embodiments, the binding interaction 130 between each pair of dopant molecules 120 is the same.In some embodiments, the binding interactions 130 between each pair of dopant molecules 120 are different.

[0035] In some embodiments, a plurality of dopant molecules 120 are separated by an average distance 140. In some embodiments, the average distance 140 is at least about 0.3 nanometers (nm), 0.4 nm, 0.5 nm, 0.6 nm, 0.7 nm, 0.8 nm, 0.9 nm, 1 nm, 2 nm, 3 nm, 4 nm, 5 nm, 6 nm, 7 nm, 8 nm, 9 nm, 10 nm, 11 nm, 12 nm, 13 nm, 14 nm, 15 nm, 16 nm, 17 nm, 18 nm, 19 nm, 20 nm, or more, up to about 20 nm, 19 nm, 18 nm, 17 nm, 16 nm, 15 nm, 14 nm, 13 nm, 12 nm, 11 nm, 10 nm, 9 nm, 8 nm, 7 nm, 6 nm, 5 nm, 4 nm, 3 nm, 2 nm, 1 nm, 0.9 nm, 0.8 nm, 0.7 nm, 0.6 nm, 0.5 nm, 0.4 nm, 0.3 nm, or less, or within a range defined by any two of the foregoing values. For example, in some embodiments, the average distance 140 is from about 0.3 nm to about 1 nm, from about 0.3 nm to about 10 nm, or from about 1 nm to about 10 nm.

[0036] In some embodiments, a plurality of dopant molecules 120 are at least about 1×10 6 dopant molecules per cubic micrometer (μm -3 )、2×10 6 μm -3 、3×10 6 μm -3 、4×10 6 μm -3 、5×10 6 μm -3 、6×10 6 μm -3 、7×10 6 μm -3 、8×10 6 μm -3 、9×10 6 μm -3 、1×10 7 μm -3 、2×10 7 μm -3 、3×107 μm -3 、 4×10 7 μm -3 、 5×10 7 μm -3 、 6×10 7 μm -3 、 7×10 7 μm -3 、 8×10 7 μm -3 、 9×10 7 μm -3 、 1×10 8 μm -3 、 2×10 8 μm -3 、 3×10 8 μm -3 、 4×10 8 μm -3 、 5×10 8 μm -3 、 6×10 8 μm -3 、 7×10 8 μm -3 、 8×10 8 μm -3 、 9×10 8 μm -3 、 1×10 9 μm -3 、 2×10 9 μm -3 、 3×10 9 μm -3 、 4×10 9 μm -3 、 5×10 9 μm -3 、 6×10 9 μm -3 、 7×10 9 μm -3 、 8×10 9 μm -3 、 9×10 9 μm -3 、 1×10 10 μm -3 、 2×10 10 μm -3 、 3×10 10 μm -3 、 4×10 10 μm -3 、 5×10 10 μm -3 、 6×10 10μm -3 、 7×10 10 μm -3 、 8×10 10 μm -3 、 9×10 10 μm -3 、 1×10 11 μm -3 、 2×10 11 μm -3 、 3×10 11 μm -3 、 4×10 11 μm -3 、 5×10 11 μm -3 、 6×10 11 μm -3 、 7×10 11 μm -3 、 8×10 11 μm -3 、 9×10 11 μm -3 、 1×10 12 μm -3 、 or more, up to about 1×10 12 μm -3 、 9×10 11 μm -3 、 8×10 11 μm -3 、 7×10 11 μm -3 、 6×10 11 μm -3 、 5×10 11 μm -3 、 4×10 11 μm -3 、 3×10 11 μm -3 、 2×10 11 μm -3 、 1×10 11 μm -3 、 9×10 10 μm -3 、 8×10 10 μm -3 、 7×10 10 μm -3 、 6×10 10 μm -3 、 5×10 10 μm -3 、 4×10 10 μm -3 、 3×10 10μm -3 、2×10 10 μm -3 、1×10 10 μm -3 、9×10 9 μm -3 、8×10 9 μm -3 、7×10 9 μm -3 、6×10 9 μm -3 、5×10 9 μm -3 、4×10 9 μm -3 、3×10 9 μm -3 、2×10 9 μm -3 、1×10 9 μm -3 、9×10 8 μm -3 、8×10 8 μm -3 、7×10 8 μm -3 、6×10 8 μm -3 、5×10 8 μm -3 、4×10 8 μm -3 、3×10 8 μm -3 、2×10 8 μm -3 、1×10 8 μm -3 、9×10 7 μm -3 、8×10 7 μm -3 、7×10 7 μm -3 、6×10 7 μm -3 、5×10 7 μm -3 、4×10 7 μm -3 、3×10 7 μm -3 、2×10 7 μm -3 、1×10 7 μm -3 、9×10 6 μm-3 、8×10 6 μm -3 、7×10 6 μm -3 、6×10 6 μm -3 、5×10 6 μm -3 、4×10 6 μm -3 、3×10 6 μm -3 、2×10 6 μm -3 、1×10 6 μm -3 、or a concentration less than or equal thereto, or a concentration within the range defined by any two of the aforementioned values, and is contained in the host material 110.

[0037] Although FIG. 1A is shown as including nine dopant molecules 120, system 100 can include any number of dopant molecules 120. For example, system 100 can include at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000, 10,000, 20,000, 30,000, 40,000, 50,000, 60,000, 70,000, 80,000, 90,000, 100,000, 200,000, 300,000, 400,000, 500,000, 600,000, 7000,000, 800,000, 900,000, 1,000,000, or more dopant molecules 120, up to about 1,000,000, 900,000, 800,000, 700,000, 600,000, 500,000, 400,000, 300,000, 200,000, 100,000, 90,000, 80,000, 70,000, 60,000, 50,000, 40,000, 30,000, 20,000, 10,000, 9,000, 8,000, 7,000, 6,000, 5,000, 4,000, 3,000, 2,000, 1,000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 dopant molecule 120, or a number of dopant molecules 120 within a range defined by any two of the foregoing values.

[0038] FIG. 1A depicts dopant molecules 120 arranged in an array, but this depiction is not intended to be limiting. In some embodiments, each of the dopant molecules 120 can have any number of nearest neighbors described herein. In some embodiments, different dopant molecules 120 can have different numbers of nearest neighbors. For example, one dopant molecule 120 can have eight nearest neighbors, and another dopant molecule 120 can have two nearest neighbors. In some embodiments, the dopant molecules 120 are arranged in a regular, irregular, or disordered array. In some embodiments, the spatial arrangement of the nearest neighbors around each of the dopant molecules 120 is different. In some embodiments, the separation between each nearest neighbor and each of the dopant molecules 120 is different.

[0039] In some embodiments, the dopant molecules 120 are generated by cleaving (e.g., photolyzing) at least one precursor to at least one of the dopant molecules 120. In some embodiments, the at least one precursor includes at least one cleavable moiety. In some embodiments, the at least one cleavable moiety includes at least one photocleavable moiety. In some embodiments, the at least one photocleavable moiety includes at least one diazo moiety. In some embodiments, the precursor includes a derivative of a carbene molecule. In some embodiments, the precursor includes a diazo derivative of a carbene molecule, or any partially or fully isotopically labeled derivative thereof.

[0040] In some embodiments, the precursor includes a diazo derivative of a diaryl carbene. In some embodiments, the precursor includes (diazomethylene)dinaphthalene, (diazomethylene)dibenzene, or any partially or fully isotopically labeled derivative thereof.

[0041] In some embodiments, at least one photocleavable moiety comprises at least one azide moiety, at least one isocyanate moiety, or at least one iminoyodine moiety. In some embodiments, the precursor comprises an azide derivative of a nitrene molecule, an isocyanate derivative of a nitrene molecule, or an iminoyodine derivative of a nitrene molecule, or any partially or fully isotopically labeled derivatives thereof.

[0042] In some embodiments, the precursor comprises 4-azidobenzoic acid or any partially or fully isotopically labeled derivatives thereof.

[0043] In some embodiments, the precursor is at least partially deuterated. That is, in some embodiments, the precursor contains one or more deuterium atoms where a hydrogen atom would otherwise be expected. In some embodiments, the precursor contains at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, or more deuterium atoms, up to about 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 deuterium atom, or the number of deuterium atoms is within a range defined by any two of the foregoing values. In some embodiments, the precursor is fully deuterated. That is, in some embodiments, the precursor contains deuterium atoms at all sites where a hydrogen atom would otherwise be expected. In some embodiments, the precursor is at least partially labeled with carbon-13. That is, in some embodiments, the precursor contains one or more carbon-13 atoms where a carbon-13 atom would otherwise be expected. In some embodiments, the precursor contains at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, or more carbon-13 atoms, up to about 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 carbon-13 atom, or the number of carbon-13 atoms is within a range defined by any two of the foregoing values.

[0044] In some embodiments, at least one photo-cleavable moiety is susceptible to cleavage from at least one precursor when exposed to cleavage (e.g., photolysis) light. In some embodiments, the cleavage light has a central wavelength of at least about 200 nanometers (nm), 210 nm, 220 nm, 230 nm, 240 nm, 250 nm, 260 nm, 270 nm, 280 nm, 290 nm, 300 nm, 310 nm, 320 nm, 330 nm, 340 nm, 350 nm, 360 nm, 370 nm, 380 nm, 390 nm, 400 nm, 410 nm, 420 nm, 430 nm, 440 nm, 450 nm, 460 nm, 470 nm, 480 nm, 490 nm, 500 nm, or more. In some embodiments, the cleavage light has a central wavelength of at most about 500 nm, 490 nm, 480 nm, 470 nm, 460 nm, 450 nm, 440 nm, 430 nm, 420 nm, 410 nm, 400 nm, 390 nm, 380 nm, 370 nm, 360 nm, 350 nm, 340 nm, 330 nm, 320 nm, 310 nm, 300 nm, 290 nm, 280 nm, 270 nm, 260 nm, 250 nm, 240 nm, 230 nm, 220 nm, 210 nm, 200 nm, or less. In some embodiments, the cleavage light has a central wavelength within a range defined by any two of the foregoing values, such as from about 300 nm to about 500 nm, from about 300 nm to about 400 nm, or from about 350 nm to about 400 nm.

[0045] Accordingly, in some embodiments, system 100 includes at least one cleaved molecule 150. In the illustrated example, system 100 includes a plurality of cleaved molecules 150. In some embodiments, at least one cleaved molecule 150 includes at least one nitrogen molecule, at least one carbon monoxide molecule, or at least one aryl iodide molecule. In some embodiments, at least one cleaved molecule 150 acts to increase the stability of at least one dopant molecule 120. For example, in some embodiments, at least one cleaved molecule 150 increases the stability of at least one dopant molecule 120 by being kinetically confined in the vicinity of other reactive dopant molecules 120. In some embodiments, at least one cleaved molecule 150 increases the stability of at least one dopant molecule 120 by reducing the chemical interaction between at least one dopant molecule 120 and the host material 110.

[0046] FIG. 1B shows a side view of system 100 according to various embodiments. In the illustrated example, system 100 includes at least one host material 110 and a plurality of dopant molecules 120.

[0047] In the illustrated embodiment, the host material 110 includes a thickness 160. In some embodiments, the host material 110 includes a thin film. That is, in some embodiments, the thickness 160 is at least about 0.3 nm, 0.4 nm, 0.5 nm, 0.6 nm, 0.7 nm, 0.8 nm, 0.9 nm, 1 nm, 2 nm, 3 nm, 4 nm, 5 nm, 6 nm, 7 nm, 8 nm, 9 nm, 10 nm, 20 nm, 30 nm, 40 nm, 50 nm, 60 nm, 70 nm, 80 nm, 90 nm, 100 nm, 200 nm, 300 nm, 400 nm, 500 nm, 600 nm, 700 nm, 800 nm, 900 nm, 1,000 nm, or more, up to about 1,000 nm, 900 nm, 800 nm, 700 nm, 600 nm, 500 nm, 400 nm, 300 nm, 200 nm, 100 nm, 90 nm, 80 nm, 70 nm, 60 nm, 50 nm, 40 nm, 30 nm, 20 nm, 10 nm, 9 nm, 8 nm, 7 nm, 6 nm, 5 nm, 4 nm, 3 nm, 2 nm, 1 nm, 0.9 nm, 0.8 nm, 0.7 nm, 0.6 nm, 0.5 nm, 0.4 nm, 0.3 nm, or less, or within a range defined by any two of the foregoing values. For example, in some embodiments, the thickness 160 is from about 0.3 nm to about 1 nm, from about 0.3 nm to about 10 nm, from about 0.3 nm to about 100 nm, from about 0.3 nm to about 1,000 nm, from about 1 nm to about 10 nm, from about 1 nm to about 10 nm, from about 1 nm to about 100 nm, from about 1 nm to about 1,000 nm, from about 10 nm to about 100 nm, from about 10 nm to about 1,000 nm, or from about 100 nm to about 1,000 nm. In some embodiments, the use of the thin film host material 110 enables the formation of a quasi-two-dimensional (quasi-2D) layer of dopant molecules 120, as described herein.

[0048] In some embodiments, the thin film is formed on a substrate (not shown in FIG. 1B). In some embodiments, the substrate includes a host material 110. In some embodiments, the substrate includes a microfabrication material such as silicon, glass, or sapphire. In some embodiments, the thin film is formed using one or more microfabrication techniques such as wet cleaning, piranha cleaning, RCA cleaning, surface passivation, spin coating, dip coating, chemical vapor deposition (CVD), atmospheric pressure CVD, low pressure CVD, ultra-high vacuum CVD, aerosol-assisted CVD, direct liquid injection CVD, hot wall CVD, cold wall CVD, microwave plasma-assisted CVD, plasma-enhanced CVD (PECVD), remote PECVD, low energy PECVD, atomic layer CVD, combustion CVD, rapid thermal CVD, photoinitiated CVD, laser CVD, vapor phase growth, physical vapor deposition, sputter deposition, evaporation deposition, pulsed laser deposition, pulsed electron deposition, atomic layer deposition, molecular beam epitaxy, etching, wet etching, dry etching, reactive ion etching (RIE), deep reactive ion etching, atomic layer etching, or self-assembly (for forming self-assembled monolayers).

[0049] In some embodiments, the host material 110 has a thickness 160 of at least about 1 nm, 2 nm, 3 nm, 4 nm, 5 nm, 6 nm, 7 nm, 8 nm, 9 nm, 10 nm, 20 nm, 30 nm, 40 nm, 50 nm, 60 nm, 70 nm, 80 nm, 90 nm, 100 nm, 200 nm, 300 nm, 400 nm, 500 nm, 600 nm, 700 nm, 800 nm, 900 nm, 1 micrometer (μm), 2 μm, 3 μm, 4 μm, 5 μm, 6 μm, 7 μm, 8 μm, 9 μm, 10 μm, 20 μm, 30 μm, 40 μm, 50 μm, 60 μm, 70 μm, 80 μm, 90 μm, 100 μm, 200 μm, 300 μm, 400 μm, 500 μm, 600 μm, 700 μm, 800 μm, 900 μm, 1 millimeter (mm), 2 mm, 3 mm, 4 mm, 5 mm, 6 mm, 7 mm, 8 mm, 9 mm, 10 mm, or more, up to about 10 mm, 9 mm, 8 mm, 7 mm, 6 mm, 5 mm, 4 mm, 3 mm, 2 mm, 1 mm, 900 μm, 800 μm, 700 μm, 600 μm, 500 μm, 400 μm, 300 μm, 200 μm, 100 μm, 90 μm, 80 μm, 70 μm, 60 μm, 50 μm, 40 μm, 30 μm, 20 μm, 10 μm, 9 μm, 8 μm, 7 μm, 6 μm, 5 μm, 4 μm, 3 μm, 2 μm, 1 μm, 900 nm, 800 nm, 700 nm, 600 nm, 500 nm, 400 nm, 300 nm, 200 nm, 100 nm, 90 nm, 80 nm, 70 nm, 60 nm, 50 nm, 40 nm, 30 nm, 20 nm, 10 nm, 9 nm, 8 nm, 7 nm, 6 nm, 5 nm, 4 nm, 3 nm, 2 nm, 1 nm, or less, or within a range defined by any two of the foregoing values. In some embodiments, the host material 110 is not formed on a substrate.

[0050] In the illustrated embodiments, a plurality of dopant molecules 120 are disposed in a pseudo-2D layer. In some embodiments, the pseudo-2D layer comprises a thin slice of space in which the plurality of dopant molecules 120 are confined. In some embodiments, vectors can be depicted between pairs of dopant molecules 120 in the pseudo-2D layer. In some embodiments, the vectors are angled with respect to a plane defined by the host material 110. In some embodiments, the angle is at least about 0 degrees, 1 degree, 2 degrees, 3 degrees, 4 degrees, 5 degrees, 6 degrees, 7 degrees, 8 degrees, 9 degrees, 10 degrees, 15 degrees, 20 degrees, 25 degrees, 30 degrees, 35 degrees, 40 degrees, 45 degrees, 50 degrees, 55 degrees, 60 degrees, 65 degrees, 70 degrees, 75 degrees, 80 degrees, 85 degrees, or 90 degrees, up to about 90 degrees, 85 degrees, 80 degrees, 75 degrees, 70 degrees, 65 degrees, 60 degrees, 55 degrees, 50 degrees, 45 degrees, 40 degrees, 35 degrees, 30 degrees, 25 degrees, 20 degrees, 15 degrees, 10 degrees, 9 degrees, 8 degrees, 7 degrees, 6 degrees, 5 degrees, 4 degrees, 3 degrees, 2 degrees, 1 degree, or 0 degrees, or within a range defined by any two of the foregoing values. In some embodiments, the pseudo-2D layer comprises a self-assembled monolayer (SAM). In some embodiments, by disposing the plurality of dopant molecules 120 in a pseudo-2D layer, the degree to which each of the plurality of dopant molecules 120 must interact with their nearest neighbors located substantially above or below them is reduced, and the quantum dynamics of the plurality of dopant molecules 120 are simplified.

[0051] FIG. 1B depicts a pseudo-2D layer that includes a thin slice of space in which a plurality of dopant molecules 120 are confined, but the disclosed embodiments are not so limited. In some embodiments, the plurality of dopant molecules 120 can be disposed in a thicker layer. In such thicker layers, each of the plurality of dopant molecules 120 can interact with their nearest neighbors located substantially above or below them.

[0052] An electronic triplet state for use as a ground state of a qubit Figure 2 shows an embodiment of the electronic energy level diagram 200 of the GST molecule. In some embodiments, the GST molecule is used as a qubit (e.g., the qubit described herein with respect to FIGS. 1A and 1B). In the illustrated embodiment, the GST molecule is associated with a GST electronic manifold 210, a first singlet electronic state 220, a second singlet electronic state 230, and an excited state triplet (EST) electronic manifold 240. In some embodiments, the GST electronic manifold 210 includes a first triplet state 211, a second triplet state 212, and a third triplet state 213. In some embodiments, the first triplet state 211, the second triplet state 212, and the third triplet state 213 represent the lowest energy electronic states of the GST molecule. In some embodiments, the first triplet state 211 is denoted as / T1>, the second triplet state 212 is denoted as / T2>, and the third triplet state 213 is denoted as / T3>. In some embodiments, the EST electronic manifold 240 includes a first triplet state 241, a second triplet state 242, and a third triplet state 243. In some embodiments, the first singlet electronic state 220, the second singlet electronic state 230, and the EST electronic manifold 240 each represent an electronic state of higher energy than the GST molecule. As shown in FIG. 2, in some embodiments, the second singlet electronic state 230 is lower in energy than the EST electronic manifold 240. However, in other embodiments, the second singlet electronic state 230 is higher in energy than the EST electronic manifold 240.

[0053] In some embodiments, at thermal equilibrium, the GST electronic state 210 is highly populated (i.e., the electronic wavefunction of the GST molecule is highly biased towards the GST electronic state 210 and has a relatively equal contribution to the first triplet state 211, the second triplet state 212, and the third triplet state 213), while the first singlet electronic state 220, the second singlet electronic state 230, the first triplet state 241, the second triplet state 242, and the third triplet state 243 are not highly populated.

[0054] In some embodiments, the GST molecule is configured to absorb electromagnetic energy and drive the population from a first triplet state 211, a second triplet state 212, or a third triplet state 213 to a first singlet electronic state 220, a second singlet electronic state 230, a first triplet state 241, a second triplet state 242, or a third triplet state 243. In some embodiments, the GST molecule is configured to relax via radiative decay back to the first triplet state 211, the second triplet state 212, or the third triplet state 213, or back to the first singlet electronic state 220 or the second singlet electronic state 230 via intersystem crossing (ISC). In some embodiments, continuous absorption of electromagnetic energy selectively drives the population to any combination of the first triplet state 211, the second triplet state 212, and the third triplet state 213, thereby generating a non-equilibrium electron state distribution. In this manner, any combination of the first triplet state 211, the second triplet state 212, and the third triplet state 213 can be "superpolarized" as described herein.

[0055] In some embodiments, a linear combination of the first triplet state / T1>, the second triplet state / T2>, and the third triplet state / T3> can be utilized as the basis state of a qubit for non-classical calculations. Thus, a qubit is the basis state of a first qubit (e.g., the basis state of the first qubit

Number

Number

[0056] In some embodiments, the lifetime (e.g., coherence lifetime or relaxation lifetime) of the ground state of the first qubit or the ground state of the second qubit is at least about 100 microseconds (μs), 200 μs, 300 μs, 400 μs, 500 μs, 600 μs, 700 μs, 800 μs, 900 μs, 1 millisecond (ms), 2 ms, 3 ms, 4 ms, 5 ms, 6 ms, 7 ms, 8 ms, 9 ms, 10 ms, 15 ms, 20 ms, 25 ms, 30 ms, 35 ms, 40 ms, 45 ms, 50 ms, 55 ms, 60 ms, 65 ms, 70 ms, 75 ms, 80 ms, 85 ms, 90 ms, 95 ms, 100 ms, 125 ms, 150 ms, 175 ms, 200 ms, 225 ms, 250 ms, 275 ms, 300 ms, 325 ms, 350 ms, 375 ms, 400 ms, 425 ms, 450 ms, 475 ms, 500 ms, 525 ms, 550 ms, 575 ms, 600 ms, 625 ms, 650 ms, 675 ms, 700 ms, 725 ms, 800 ms, 825 ms, 850 ms, 875 ms, 900 ms, 925 ms, 950 ms, 975 ms, 1 second (s), 2 s, 3 s, 4 s, 5 s, 6 s, 7 s, 8 s, 9 s, 10 s, 20 s, 30 s, 40 s, 50 s, 1 minute (min), 2 min, 3 min, 4 min, 5 min, 6 min, 7 min, 8 min, 9 min, 10 min, 20 min, 30 min, 40 min, 50 min, 1 hour (h), 2 h, 3 h, 4 h, 5 h, 6 h, 7 h, 8 h, 9 h, 10 h, or more, up to about 10 h, 9 h, 8 h, 7 h, 6 h, 5 h, 4 h, 3 h, 2 h, 1 h, 50 min, 40 min, 30 min, 20 min, 10 min, 9 min, 8 min, 7 min, 6 min, 5 min, 4 min, 3 min, 2 min, 1 min, 50 s, 40 s, 30 s, 20 s, 10 s, 9 s, 8 s, 7 s, 6 s, 5 s, 4 s, 3 s, 2 s, 1 s, 975 ms, 950 ms, 925 ms, 900 ms, 875 ms, 850 ms, 825 ms, 800 ms, 775 ms, 750 ms, 725 ms, 700 ms, 675 ms, 650 ms, 625 ms, 600 ms, 575 ms, 550 ms, 525 ms, 500 ms, 475 ms, 450 ms, 425 ms, 400 ms, 375 ms, 350 ms, 325 ms, 300 ms, 275 ms, 250 ms, 225 ms, 200 ms, 175 ms, 150 ms,A lifetime of 125 ms, 100 ms, 95 ms, 90 ms, 85 ms, 80 ms, 75 ms, 70 ms, 65 ms, 60 ms, 55 ms, 50 ms, 45 ms, 40 ms, 35 ms, 30 ms, 25 ms, 20 ms, 15 ms, 10 ms, 9 ms, 8 ms, 7 ms, 6 ms, 5 ms, 4 ms, 3 ms, 2 ms, 1 ms, 900 μs, 800 μs, 700 μs, 600 μs, 500 μs, 400 μs, 300 μs, 200 μs, 100 μs, or less, or within a range defined by any two of the foregoing values.

[0057] In some embodiments, the lifetime is defined as a half-life for the electronic state of the qubit to return from a superpolarized electron state distribution to a thermal equilibrium electron state distribution. In some embodiments, the lifetime is measured at an intended operating temperature of the qubit of at least about 1 K, 2 K, 3 K, 4 K, 5 K, 6 K, 7 K, 8 K, 9 K, 10 K, 15 K, 20 K, 25 K, 30 K, 35 K, 40 K, 45 K, 50 K, or more, up to about 50 K, 45 K, 40 K, 35 K, 30 K, 25 K, 20 K, 15 K, 10 K, 9 K, 8 K, 7 K, 6 K, 5 K, 4 K, 3 K, 2 K, 1 K, or less, or between any two of the foregoing values (such as about 4 K to about 20 K). In some embodiments, the coupling strength described herein with respect to FIGS. 1A and 1B (e.g., the coupling interaction 130 shown in FIGS. 1A and 1B) is greater than a multiple of the reciprocal of the lifetime. In some embodiments, the multiple is at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more, up to about 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, or less, or within a range defined by any two of the foregoing values.

[0058] Optical Superpolarization and Initialization of Qubit States In some embodiments, hyperpolarization enables non-classical calculations to be performed with a high signal-to-noise ratio (SNR). In some embodiments, hyperpolarization enables initialization of non-classical calculations by initializing a qubit in the ground state of a first qubit or the ground state of a second qubit (or any linear combination thereof). In some embodiments, hyperpolarization enables coherent manipulation of the quantum state of qubits for performing non-classical calculations.

[0059] In some embodiments, hyperpolarization enables placement of one or more qubits in a particular quantum state (e.g., the ground state of a first qubit, the ground state of a second qubit, or any linear combination thereof). In some embodiments, the qubits are initialized after such hyperpolarization.

[0060] In the context of GST molecules, in some embodiments, hyperpolarization describes a state where the absolute value of the difference between a population of electronic states in one state (e.g., the first singlet electronic state of a GST molecule) and a population of electronic states in another state (e.g., any combination of the first triplet state / T1>, the second triplet state / T2>, and the third triplet state / T3> of a GST molecule) exceeds the absolute value of the corresponding difference at thermal equilibrium.

[0061] In some embodiments, the population difference between two electronic states is the difference between the populations of the two electronic states divided by the total population of the two electronic states. The population difference can be expressed as a fractional population difference or a percentage population difference. In some embodiments, the population difference (expressed as a percentage) is at least about 1%, 2%, 3%, 4%, 5%, 6%, 7%, 8%, 9%, 10%, 15%, 20%, 25%, 30%, 35%, 40%, 45%, 50%, 55%, 60%, 65%, 70%, 75%, 80%, 85%, 90%, 95% or more, up to about 95%, 90%, 85%, 80%, 75%, 70%, 65%, 60%, 55%, 50%, 45%, 40%, 35%, 30%, 25%, 20%, 15%, 10%, 9%, 8%, 7%, 6%, 5%, 4%, 3%, 2%, 1% or less, or within a range defined by any two of the foregoing values.

[0062] As described herein, in some embodiments, the qubits are configured to absorb electromagnetic energy and drive the population to any combination of a first triplet state / T1>, a second triplet state / T2>, and a third triplet state / T3>, thereby generating superpolarization. In some embodiments, the electromagnetic energy has a central wavelength selected to drive the population to any combination of a first triplet state / T1>, a second triplet state / T2>, and a third triplet state / T3>. In some embodiments, the central wavelength is within the infrared (IR), visible, or ultraviolet (UV) portion of the electromagnetic spectrum. In some embodiments, the central wavelength is at least about 200 nm, 210 nm, 220 nm, 230 nm, 240 nm, 250 nm, 260 nm, 270 nm, 280 nm, 290 nm, 300 nm, 310 nm, 320 nm, 330 nm, 340 nm, 350 nm, 360 nm, 370 nm, 380 nm, 390 nm, 400 nm, 410 nm, 420 nm, 430 nm, 440 nm, 450 nm, 460 nm, 470 nm, 480 nm, 490 nm, 500 nm, 510 nm, 520 nm, 530 nm, 540 nm, 550 nm, 560 nm, 570 nm, 580 nm, 590 nm, 600 nm, 610 nm, 620 nm, 630 nm, 640 nm, 650 nm, 660 nm, 670 nm, 680 nm, 685 nm, 690 nm, 700 nm, 710 nm, 720 nm, 730 nm, 740 nm, 750 nm, 760 nm, 770 nm, 780 nm, 790 nm, 800 nm, 810 nm, 820 nm, 830 nm, 840 nm, 850 nm, 860 nm, 870 nm, 880 nm, 890 nm, 900 nm, 910 nm, 920 nm, 930 nm, 940 nm, 950 nm, 960 nm, 970 nm, 980 nm, 990 nm, 1,000 nm, or more, up to about 1,000 nm, 990 nm, 980 nm, 970 nm, 960 nm, 950 nm, 940 nm, 930 nm, 920 nm, 910 nm, 900 nm, 890 nm, 880 nm, 870 nm, 860 nm, 850 nm, 840 nm, 830 nm, 820 nm, 810 nm, 800 nm, 790 nm, 780 nm, 770 nm, 760 nm, 750 nm, 740 nm, 730 nm, 720 nm, 710 nm, 700 nm, 690 nm, 680 nm, 670 nm, 660 nm, 650 nm, 640 nm, 630 nm, 620 nm, 610 nm, 600 nm, 590 nm, 580 nm, 570 nm, 560 nm, 550 nm, 540 nm, 530 nm, 520 nm, 510 nm, 500 nm, 490 nm, 480 nm, 470 nm, 460 nm, 450 nm, 440 nm, 430 nm, 420 nm, 410 nm, 400 nm, 390 nm, 380 nm, 370 nm, 360 nm, 350 nm, 340 nm, 330 nm, 320 nm, 310 nm, 300 nm, 290 nm, 280 nm, 270 nm, 260 nm, 250 nm, 240 nm, 230 nm, 220 nm, 210 nm, 200 nm, or less, or within a range defined by any two of the foregoing values.,

[0063] Optical initialization of individual qubits Returning to the discussion of FIGS. 1A and 1B, in some embodiments, different dopant molecules 120 experience different physicochemical environments because they have different positions or orientations within the host material 110. In some embodiments, the different physicochemical environments cause different dopant molecules 120 to have slightly different electronic energy level structures. For example, returning to the discussion of FIG. 2, the energy difference between any two of the first triplet state 211, the second triplet state 212, the third triplet state 213, the first singlet electron state 220, the second singlet state 230, the first triplet state 241, the second triplet state 242, and the third triplet state 243 may depend on the physicochemical environment of the associated dopant molecule and may shift the wavelength or frequency of the electromagnetic energy required to drive a transition between those two states.,

[0064] Returning to the discussion of FIGS. 1A and 1B, in some embodiments, the different electronic energy level structures of the dopant molecules 120 may allow for individual addressing of each dopant molecule 120. For example, if the bandwidth of the optical energy used to initialize each dopant molecule is narrow enough (e.g., small compared to the difference between the wavelength required to initialize a given dopant molecule 120 and the wavelength required to initialize another dopant molecule 120), each dopant molecule 120 can be optically addressed individually.

[0065] For example, the first dopant molecule 120 and the second dopant molecule 120 may have different electronic energy level structures. Thus, in some embodiments, the first dopant molecule 120 may be configured to absorb first electromagnetic energy having a first center wavelength, and the second dopant molecule 120 may be configured to absorb second electromagnetic energy having a second center wavelength. In some embodiments, the first or second center wavelength includes any center wavelength described herein. In some embodiments, the first and second center wavelengths are different from each other.

[0066] In some embodiments, the first central wavelength is associated with a first wavelength range having a first bandwidth. In some embodiments, the first bandwidth is measured as a first full width at half maximum (FWHM). In some embodiments, the second central wavelength is associated with a second wavelength range having a second bandwidth. In some embodiments, the second bandwidth is measured as a second FWHM bandwidth. In some embodiments, the first bandwidth or the second bandwidth is at least about 1 MHz, 2 MHz, 3 MHz, 4 MHz, 5 MHz, 6 MHz, 7 MHz, 8 MHz, 9 MHz, 10 MHz, 15 MHz, 20 MHz, 25 MHz, 30 MHz, 35 MHz, 40 MHz, 45 MHz, 50 MHz, 55 MHz, 60 MHz, 65 MHz, 70 MHz, 75 MHz, 80 MHz, 85 MHz, 90 MHz, 95 MHz, 100 MHz, or more, up to about 100 MHz, 95 MHz, 90 MHz, 85 MHz, 80 MHz, 75 MHz, 70 MHz, 65 MHz, 60 MHz, 55 MHz, 50 MHz, 45 MHz, 40 MHz, 35 MHz, 30 MHz, 25 MHz, 20 MHz, 15 MHz, 10 MHz, 9 MHz, 8 MHz, 7 MHz, 6 MHz, 5 MHz, 4 MHz, 3 MHz, 2 MHz, 1 MHz, or less, or within a range defined by any two of the foregoing values.

[0067] In some embodiments, the first wavelength range and the second wavelength range are different. In some embodiments, the first wavelength range and the second wavelength range do not overlap (e.g., within the first FWHM and the second FWHM). In some embodiments, the first FWHM and the second FWHM are similar to or broader than the bandwidth of the light source directed at the first dopant molecule 120 and the second dopant molecule 120. In some embodiments, the non-overlapping nature of the first wavelength range and the second wavelength range allows the first dopant molecule 120 to absorb optical energy, while the second dopant molecule 120 does not absorb optical energy. In some embodiments, the non-overlapping nature of the first wavelength range and the second wavelength range allows the second dopant molecule 120 to absorb optical energy, while the first dopant molecule 120 does not absorb optical energy. This procedure may be referred to as "individual optical initialization" of the first and second dopant molecules 120. In some embodiments, the individual optical initialization of the first and second dopant molecules 120 causes different amounts of optical energy to be emitted to the first and second dopant molecules 120. In some embodiments, measuring the optical energy collapses the quantum state of at least one dopant molecule to the electronic energy eigenstate of at least one dopant molecule, thereby initializing the dopant molecule to the desired initial quantum state.

[0068] Although discussed in terms of two dopant molecules 120, the individual principles of optical initialization described herein can be extended to any number of dopant molecules 120. For example, an individual optical initialization can be for at least about 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000, 10,000, or more dopant molecules 120, up to about 10,000, 9,000, 6,000, 5,000, 4,000, 3,000, 2,000, 1,000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 9, 8, 7, 6, 5, 4, 3, or 2 dopant molecules 120, or a number of dopant molecules 120 within a range defined by any two of the foregoing values.

[0069] Such individual optical initializations can be particularly useful for qubits based on dopant molecules 120. As described herein, such dopant molecules 120 can be separated from each other by a relatively small distance compared to a typical optical beam waist. For example, in some embodiments, the dopant molecules 120 are separated from each other by a distance of less than 10 nm (or any other separation distance described herein) to ensure a suitable coupling between neighboring dopant molecules 120. In some embodiments, a typical optical beam waist may be about 500 nm such that the optical energy impinges on about 5,000 qubits. Thus, individual optical initializations can enable the manipulation of individual qubits even when the optical energy is directed at hundreds or thousands of qubits.

[0070] In some embodiments, the individual optical initialization of a qubit enables the individual initialization of the qubit in the ground state of the first qubit or the ground state of the second qubit (or any linear combination thereof), thereby enabling the initialization of a non - classical computation.

[0071] RF or MW operation of individual qubits In some embodiments, the first and second qubit states described herein are separated by an energy difference in the RF or MW portion of the electromagnetic spectrum. Thus, in some embodiments, the manipulation of the quantum state of each qubit can be performed using RF energy or MW energy. Further, in some embodiments, the different physicochemical environments of the different dopant molecules 120 result in a wavelength or frequency shift that is not large enough to enable individual optical initialization of each qubit. In such embodiments, multiple qubits can be optically initialized simultaneously, for example using a broadband light source, as described herein. In some embodiments, the quantum state of each qubit is then individually manipulated using RF energy or MW energy.

[0072] In some embodiments, the first dopant molecule 120 can be configured to absorb first electromagnetic energy having a first center frequency, and the second dopant molecule 120 can be configured to absorb second electromagnetic energy having a second center frequency. In some embodiments, the first or second center frequency is at least about 1 MHz, 2 MHz, 3 MHz, 4 MHz, 5 MHz, 6 MHz, 7 MHz, 8 MHz, 9 MHz, 10 MHz, 20 MHz, 30 MHz, 40 MHz, 50 MHz, 60 MHz, 70 MHz, 80 MHz, 90 MHz, 100 MHz, 200 MHz, 300 MHz, 400 MHz, 500 MHz, 600 MHz, 700 MHz, 800 MHz, 900 MHz, 1 gigahertz (GHz), 2 GHz, 3 GHz, 4 GHz, 5 GHz, 6 GHz, 7 GHz, 8 GHz, 9 GHz, 10 GHz, 20 GHz, 30 GHz, 40 GHz, 50 GHz, 60 GHz, 70 GHz, 80 GHz, 90 GHz, 100 GHz, or more, up to about 100 GHz, 90 GHz, 80 GHz, 70 GHz, 60 GHz, 50 GHz, 40 GHz, 30 GHz, 20 GHz, 10 GHz, 9 GHz, 8 GHz, 7 GHz, 6 GHz, 5 GHz, 4 GHz, 3 GHz, 2 GHz, 1 GHz, 900 MHz, 800 MHz, 700 MHz, 600 MHz, 500 MHz, 400 MHz, 300 MHz, 200 MHz, 100 MHz, 90 MHz, 80 MHz, 70 MHz, 60 MHz, 50 MHz, 40 MHz, 30 MHz, 20 MHz, 10 MHz, 9 MHz, 8 MHz, 7 MHz, 6 MHz, 5 MHz, 4 MHz, 3 MHz, 2 MHz, 1 MHz, or less, or within a range defined by any two of the foregoing values. In some embodiments, the first or second center frequency is within the RF or MW portion of the electromagnetic spectrum.

[0073] In some embodiments, the first and second center frequencies are different from each other. In some embodiments, the first center frequency is associated with a first frequency range having a first bandwidth. In some embodiments, the first bandwidth is measured as a first FWHM bandwidth. In some embodiments, the second center frequency is associated with a second frequency range having a second bandwidth. In some embodiments, the second bandwidth is measured as a second FWHM bandwidth. In some embodiments, the first or second bandwidth depends on the power of the RF energy or MW energy supplied to the first or second dopant molecule 120. In some embodiments, the first or second bandwidth includes the natural bandwidth of the first or second dopant molecule 120.For example, in some embodiments, the first or second bandwidth is at least about 100 Hz, 200 Hz, 300 Hz, 400 Hz, 500 Hz, 600 Hz, 700 Hz, 800 Hz, 900 Hz, 1 kHz, 2 kHz, 3 kHz, 4 kHz, 5 kHz, 6 kHz, 7 kHz, 8 kHz, 9 kHz, 10 kHz, 20 kHz, 30 kHz, 40 kHz, 50 kHz, 60 kHz, 70 kHz, 80 kHz, 90 kHz, 100 kHz, 200 kHz, 300 kHz, 400 kHz, 500 kHz, 600 kHz, 700 kHz, 800 kHz, 900 kHz, 1 MHz, 2 MHz, 3 MHz, 4 MHz, 5 MHz, 6 MHz, 7 MHz, 8 MHz, 9 MHz, 10 MHz, 20 MHz, 30 MHz, 40 MHz, 50 MHz, 60 MHz, 70 MHz, 80 MHz, 90 MHz, 100 MHz, or more, up to about 100 MHz, 90 MHz, 80 MHz, 70 MHz, 60 MHz, 50 MHz, 40 MHz, 30 MHz, 20 MHz, 10 MHz, 9 MHz, 8 MHz, 7 MHz, 6 MHz, 5 MHz, 4 MHz, 3 MHz, 2 MHz, 1 MHz, 900 kHz, 800 kHz, 700 kHz, 600 kHz, 500 kHz, 400 kHz, 300 kHz, 200 kHz, 100 kHz, 90 kHz, 80 kHz, 70 kHz, 60 kHz, 50 kHz, 40 kHz, 30 kHz, 20 kHz, 10 kHz, 9 kHz, 8 kHz, 7 kHz, 6 kHz, 5 kHz, 4 kHz, 3 kHz, 2 kHz, 1 kHz, 900 Hz, 800 Hz, 700 Hz, 600 Hz, 500 Hz, 400 Hz, 300 Hz, 200 Hz, 100 Hz, or less, or within a range defined by any two of the foregoing values.

[0074] In some embodiments, the first frequency range and the second frequency range are different. In some embodiments, the first frequency range and the second frequency range do not overlap (e.g., within the first FWHM and the second FWHM). In some embodiments, the first FWHM and the second FWHM are similar to or narrower than the bandwidth of the RF energy or MW energy directed at the first dopant molecule 120 and the second dopant molecule 120. In some embodiments, the non-overlapping nature of the first frequency range and the second frequency range allows the first dopant molecule 120 to absorb RF energy or MW energy while the second dopant molecule 120 does not absorb RF energy or MW energy. In some embodiments, the non-overlapping nature of the first frequency range and the second frequency range allows the second dopant molecule 120 to absorb RF energy or MW energy while the first dopant molecule 120 does not absorb RF energy or MW energy. This procedure may be referred to as "individual RF or MW manipulation" of the first and second dopant molecules 120.

[0075] Although discussed in terms of two dopant molecules 120, the principles of the individual RF or MW manipulation described herein can be extended to any number of dopant molecules 120. For example, the individual RF or MW manipulation can be applied to at least about 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000, 10,000, or more dopant molecules 120, up to about 10,000, 9,000, 8,000, 7,000, 6,000, 5,000, 4,000, 3,000, 2,000, 1,000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 9, 8, 7, 6, 5, 4, 3, or 2 dopant molecules 120, or a number of dopant molecules 120 within a range defined by any two of the foregoing values.

[0076] Such individual RF or MW operations can be particularly useful for qubits based on dopant molecules 120. As described herein, such dopant molecules 120 can be separated from each other by a relatively small distance compared to a typical optical beam waist. For example, in some embodiments, the dopant molecules 120 are separated from each other by a distance of less than 10 nm (or any other separation distance described herein) to ensure a suitable coupling between neighboring dopant molecules 120. In some embodiments, a typical optical beam waist may be on the order of hundreds or thousands of qubits, as described herein.

[0077] Accordingly, individual RF or MW operations can enable individual coherent operations of the quantum state of each qubit after (individual or simultaneous) optical initialization of the qubits. In some embodiments, the coherent operations include the implementation of at least one non-classical operation. In some embodiments, the non-classical operation includes any non-classical operation described herein.

[0078] Storage of non-classical information in nuclear spin degrees of freedom In some embodiments, non-classical information (such as that obtained during or after the implementation of any of the non-classical operations described herein) can be transferred from the electronic state of at least one dopant molecule 120 to the nuclear spin state of at least one dopant molecule 120, or at least one nearby molecule (referred to as a "nearby host molecule") contained within the host material 110. In some embodiments, the information can be transferred by implementing a swap gate between the electronic state and the nuclear spin state of at least one dopant molecule 120. In some embodiments, the swap gate can be implemented by applying RF energy or MW energy to at least one dopant molecule 120 and the nuclear spin state, as described herein.

[0079] In some embodiments, transmitting non-classical information into the nuclear spin state provides an increase in readout fidelity, initialization fidelity, or lifetime, thereby improving the overall fidelity of non-classical computing.

[0080] Optical readout of individual qubits In some embodiments, the different electronic energy level structures of the dopant molecules 120 may enable individual optical readout of the quantum states of each dopant molecule 120 after non-classical operation. For example, the quantum state of each dopant molecule 120 may be optically read out individually based on the wavelength of the light emitted by the dopant molecule 120, which may vary based on the physicochemical environment of each dopant molecule 120.

[0081] In some embodiments, each dopant molecule 120 is configured to absorb and emit light. In some embodiments, the optical properties of the light emitted by each dopant molecule 120 correlate with the quantum state of the associated dopant molecule 120. For example, in some embodiments, a dopant molecule 120 in a first qubit state absorbs and emits light having a first property, while a dopant molecule 120 in a second qubit state absorbs and emits light having a second property. In some embodiments, a dopant molecule in a linear superposition between a first qubit state and a second qubit state absorbs and emits light having a linear superposition of the first property and the second property. In some embodiments, the first property is different from the second property. Thus, in some embodiments, measuring the light emitted by the dopant molecule 120 enables determination of the quantum state of the dopant molecule 120 at the time of measurement. In some embodiments, the first or second property includes the intensity of the light emitted by the dopant molecule 120. In some embodiments, the first or second property includes the polarization state of the light emitted by the dopant molecule 120. In some embodiments, the first or second property includes the wavelength of the light emitted by the dopant molecule 120. In some embodiments, the first or second property includes the frequency of the light emitted by the dopant molecule 120.

[0082] System for initializing, manipulating, and reading out the qubit state of dopant molecules Figure 3 shows a system 300 for performing non-classical computing using the system 100 of FIG. 1A or FIG. 1B, according to various embodiments. In the illustrated example, system 300 includes at least one cryogenic unit 310. In some embodiments, cryogenic unit 310 is configured to include the system 100 described herein with respect to FIGS. 1A and 1B. In some embodiments, cryogenic unit 310 includes system 100. In some embodiments, cryogenic unit 310 does not include system 100. In some embodiments, cryogenic unit 310 is configured to cool system 100 to an operating temperature of at least about 1K, 2K, 3K, 4K, 5K, 6K, 7K, 8K, 9K, 10K, 15K, 20K, 25K, 30K, 35K, 40K, 45K, 50K, or more, up to about 50K, 45K, 40K, 35K, 30K, 25K, 20K, 15K, 10K, 9K, 8K, 7K, 6K, 5K, 4K, 3K, 2K, 1K, or less, or a temperature between any two of the foregoing values (such as about 4K to about 20K). In some embodiments, cryogenic unit 310 includes at least one helium cryocooler. In some embodiments, cryogenic unit 310 includes at least one closed-cycle helium cryocooler. In some embodiments, cryogenic unit 310 includes at least one window (not shown in FIG. 3) configured to allow electromagnetic energy (such as optical energy) to pass through it. In some embodiments, cryogenic unit 310 includes at least one electrical feedthrough (not shown in FIG. 3) configured to allow electromagnetic energy (such as RF energy or MW energy) to pass through it.

[0083] In the illustrated embodiment, system 300 includes at least one initialization unit 320. In some embodiments, initialization unit 320 is configured to direct a third electromagnetic energy 322 towards at least one dopant molecule (not shown in FIG. 3) of system 100. In some embodiments, third electromagnetic energy 322 is configured to initialize the quantum state of at least one dopant molecule into any linear combination of a first qubit state and a second qubit state, as described herein with respect to FIGS. 1A, 1B, and 2. In some embodiments, third electromagnetic energy 322 includes at least one IR wavelength, visible wavelength, or UV wavelength described herein. For example, in some embodiments, third electromagnetic energy 322 includes at least one wavelength from about 200 nm to about 1,000 nm. In some embodiments, initialization unit 320 is configured to initialize the quantum state of at least one dopant molecule in any manner described herein with respect to FIGS. 1A, 1B, or 2. In some embodiments, initialization unit 320 comprises a confocal optical system, a confocal microscope, or a wide-field microscope. In some embodiments, initialization unit 320 is configured to measure electromagnetic energy (not shown in FIG. 3) emitted by at least one dopant molecule in response to third electromagnetic energy 322. In some embodiments, the measured electromagnetic energy indicates whether the quantum state of at least one dopant molecule has been properly initialized. In some embodiments, measuring the emitted electromagnetic energy collapses the quantum state of at least one dopant molecule into an electronic energy eigenstate of at least one dopant molecule, thereby initializing the dopant molecule into a desired initial quantum state. In some embodiments, initialization unit 320 is configured to reapply third electromagnetic energy 322 in response to the measured electromagnetic energy. For example, in some embodiments, initialization unit 320 is configured to reapply third electromagnetic energy 322 to at least one dopant molecule if the measured electromagnetic energy indicates that at least one dopant molecule has not been properly initialized.

[0084] In the illustrated embodiment, system 300 includes a single initialization unit 320. However, in some embodiments, system 300 includes multiple initialization units 320. In some embodiments, system 300 includes at least 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000, 10,000, 20,000, 30,000, 40,000, 50,000, 60,000, 70,000, 80,000, 90,000, 100,000 or more initialization units 320, up to about 100,000, 90,000, 80,000, 70,000, 60,000, 50,000, 40,000, 30,000, 20,000, 10,000, 9,000, 8,000, 7,000, 6,000, 5,000, 4,000, 3,000, 2,000, 1,000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 initialization unit 320, or a number of initialization units 320 within a range defined by any two of the foregoing values. In some embodiments, each initialization unit 320 is configured to initialize the quantum state of at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000, 10,000 or more qubits, up to about 10,000, 9,000, 8,000, 7,000, 6,000, 5,000, 4,000, 3,000, 2,000, 1,000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 qubit, or a number of qubits within a range defined by any two of the foregoing values.

[0085] In the illustrated embodiment, system 300 comprises at least one non-classical operation unit 330. In some embodiments, the non-classical operation unit 330 is configured to apply a fourth electromagnetic energy 332 to at least one dopant molecule of system 100. In some embodiments, the fourth electromagnetic energy 332 is configured to perform at least one non-classical operation on at least one dopant molecule as described herein with respect to FIGS. 1A, 1B, and 2. In some embodiments, the fourth electromagnetic energy 332 includes at least one RF frequency or MW frequency described herein. For example, in some embodiments, the fourth electromagnetic energy 332 includes at least one frequency from about 1 MHz to about 100 GHz. In some embodiments, the non-classical operation unit is configured to perform any non-classical operation described in any manner described herein with respect to FIGS. 1A, 1B, or 2. In some embodiments, the non-classical operation unit 330 comprises at least one RF cavity, MW cavity, RF stripline, MW stripline, RF antenna, MW antenna, microscopic RF antenna, microscopic MW antenna, nanoscopic RF antenna, or nanoscopic MW antenna.

[0086] In the illustrated embodiment, system 300 comprises a single non-classical operation unit 330. However, in some embodiments, system 300 comprises multiple non-classical operation units 330. In some embodiments, system 300 comprises at least 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, or more non-classical operation units 330, up to about 1,000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 non-classical operation unit 330, or a number of non-classical operation units 330 within a range defined by any two of the foregoing values. In some embodiments, each non-classical operation unit 330 is configured to perform non-classical operations on at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, or more qubits, up to about 1,000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 qubit, or a number of qubits within a range defined by any two of the foregoing values.

[0087] In the illustrated embodiment, system 300 includes at least one storage unit 340. In some embodiments, at least one storage unit 340 is configured to apply a fifth electromagnetic energy 342 and a sixth electromagnetic energy 344 to at least one dopant molecule. In some embodiments, as described herein with respect to FIGS. 1A, 1B, and 2, the fifth electromagnetic energy 342 and the sixth electromagnetic energy 344 together are configured to transfer information from the electronic state of at least one dopant molecule to the nuclear spin state of at least one dopant molecule. In some embodiments, as described herein with respect to FIGS. 1A, 1B, and 2, the fifth electromagnetic energy 342 and the sixth electromagnetic energy 344 together are configured to apply a swap gate to at least one dopant molecule. In some embodiments, the fifth electromagnetic energy 342 includes at least one RF frequency or MW frequency described herein. For example, in some embodiments, the fifth electromagnetic energy 342 includes at least one frequency from about 1 kHz to about 100 MHz. In some embodiments, the sixth electromagnetic energy 344 includes at least one RF frequency or MW frequency described herein. For example, in some embodiments, the sixth electromagnetic energy 344 includes at least one frequency from about 1 MHz to about 100 GHz. In some embodiments, the storage unit 340 comprises at least one RF cavity, MW cavity, RF stripline, MW stripline, RF antenna, MW antenna, microscopic RF antenna, microscopic MW antenna, nanoscopic RF antenna, or nanoscopic MW antenna.

[0088] In the illustrated embodiment, system 300 includes a single storage unit 340. However, in some embodiments, system 300 includes multiple storage units 340. In some embodiments, system 300 includes at least 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, or more storage units 340, up to about 1,000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 storage unit 340, or a number of storage units 340 within a range defined by any two of the foregoing values. In some embodiments, each storage unit 340 is configured to transfer information from an electronic state to a nuclear spin state of at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, or more qubits, up to about 1,000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 qubit, or a number of qubits within a range defined by any two of the foregoing values.

[0089] In some embodiments, system 300 does not include a storage unit 340.

[0090] In the illustrated embodiment, system 300 includes at least one detection unit 350. In some embodiments, detection unit 350 is configured to detect the electronic state of at least one dopant molecule as described herein with respect to FIGS. 1A, 1B, and 2. In some embodiments, detection unit 350 is configured to detect the nuclear spin state of at least one dopant molecule as described herein with respect to FIGS. 1A, 1B, and 2. In some embodiments, detection unit 350 is configured to direct a seventh electromagnetic energy 352 towards at least one dopant molecule, thereby obtaining a result of at least one non-classical operation, as described herein with respect to FIGS. 1A, 1B, and 2. In some embodiments, the seventh electromagnetic energy 352 includes at least one IR wavelength, visible wavelength, or UV wavelength described herein. For example, in some embodiments, the seventh electromagnetic energy 352 includes at least one wavelength from about 200 nm to about 1,000 nm. In some embodiments, detection unit 350 includes at least one optical detector configured to detect light emitted by at least one dopant molecule in response to the seventh electromagnetic energy 352. In some embodiments, detection unit 350 comprises a confocal optical system, a confocal microscope, a wide-field microscope, a spectrometer, an optical spectrometer, a fluorescence spectrometer, a UV-visible spectrometer, a polarimeter, or a polarimetric camera.

[0091] In the illustrated embodiment, system 300 comprises a single detection unit 350. However, in some embodiments, system 300 comprises a plurality of detection units 350. In some embodiments, system 300 comprises at least 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000, 10,000, 20,000, 30,000, 40,000, 50,000, 60,000, 70,000, 80,000, 90,000, 100,000, or more detection units 350, up to about 100,000, 90,000, 80,000, 70,000, 60,000, 50,000, 40,000, 30,000, 20,000, 10,000, 9,000, 8,000, 7,000, 6,000, 5,000, 4,000, 3,000, 2,000, 1,000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 detection unit 350, or a number of detection units 350 within a range defined by any two of the foregoing values. In some embodiments, each detection unit 350 is configured to detect the electronic state or nuclear spin state of at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000, 10,000, or more qubits, up to about 10,000, 9,000, 8,000, 7,000, 6,000, 5,000, 4,000, 3,000, 2,000, 1,000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 qubit, or a number of qubits within a range defined by any two of the foregoing values.

[0092] In some embodiments, system 300 comprises at least one polarization beam splitter 360. In some embodiments, the polarization beam splitter 360 is configured to direct a third electromagnetic energy 322 from the initialization unit 320 towards the system 100. In some embodiments, the polarization beam splitter 360 is configured to direct a seventh electromagnetic energy 352 from the detection unit 350 towards the system 100 and, in response to the seventh electromagnetic energy 352, direct light emitted by at least one dopant molecule from the system 100 towards the detection unit 350.

[0093] In some embodiments, system 300 includes one or more magnetic field sources (not shown in FIG. 3). In some embodiments, the magnetic field sources are configured to generate one or more magnetic fields or magnetic field gradients near system 100. In some embodiments, each of the magnetic field sources includes a permanent magnet, an electromagnet, or a superconducting magnet. In some embodiments, the magnetic field sources include one or more solenoids, Helmholtz coils, anti-Helmholtz coils, saddle coils, Halbach arrays, and the like. In some embodiments, one or more of the magnetic field sources are included within cryogenic unit 310. In some embodiments, one or more of the magnetic field sources generate an average magnetic field strength (across system 100) of at least about 1 microtesla (μT), 2 μT, 3 μT, 4 μT, 5 μT, 6 μT, 7 μT, 8 μT, 9 μT, 10 μT, 20 μT, 30 μT, 40 μT, 50 μT, 60 μT, 70 μT, 80 μT, 90 μT, 100 μT, 200 μT, 300 μT, 400 μT, 500 μT, 600 μT, 700 μT, 800 μT, 900 μT, 1 millitesla (mT), 2 mT, 3 mT, 4 mT, 5 mT, 6 mT, 7 mT, 8 mT, 9 mT, 10 mT, 20 mT, 30 mT, 40 mT, 50 mT, 60 mT, 70 mT, 80 mT, 90 mT, 100 mT, 200 mT, 300 mT, 400 mT, 500 mT, 600 mT, 700 mT, 800 mT, 900 mT, 1 tesla (T), or more, up to about 1 T, 900 mT, 800 mT, 700 mT, 600 mT, 500 mT, 400 mT, 300 mT, 200 mT, 100 mT, 90 mT, 80 mT, 70 mT, 60 mT, 50 mT, 40 mT, 30 mT, 20 mT, 10 mT, 9 mT, 8 mT, 7 mT, 6 mT, 5 mT, 4 mT, 3 mT, 2 mT, 1 mT, 900 μT, 800 μT, 700 μT, 600 μT, 500 μT, 400 μT, 300 μT, 200 μT, 100 μT, 90 μT, 80 μT, 70 μT, 60 μT, 50 μT, 40 μT, 30 μT, 20 μT, 10 μT, 9 μT, 8 μT, 7 μT, 6 μT, 5 μT, 4 μT, 3 μT, 2 μT, 1 μT, or less, or an average magnetic field strength within a range defined by any two of the foregoing values. In some embodiments, one or more of the magnetic field sources have an average magnetic field gradient (across system 100) of at least about 1 microtesla per meter (μTm -1 ), 2 μTm-1 、3 μT m -1 、4 μT m -1 、5 μT m -1 、6 μT m -1 、7 μT m -1 、8 μT m -1 、9 μT m -1 、10 μT m -1 、20 μT m -1 、30 μT m -1 、40 μT m -1 、50 μT m -1 、60 μT m -1 、70 μT m -1 、80 μT m -1 、90 μT m -1 、100 μT m -1 、200 μT m -1 、300 μT m -1 、400 μT m -1 、500 μT m -1 、600 μT m -1 、700 μT m -1 、800 μT m -1 、900 μT m -1 、1 microtesla per meter (mT m -1 )、2 mT m -1 、3 mT m -1 、4 mT m -1 、5 mT m -1 、6 mT m -1 、7 mT m -1 、8 mT m -1 、9 mT m -1 、10 mT m -1 、20 mT m -1 、30 mT m -1 、40 mT m -1 、50 mT m -1 、60 mT m -1 、70 mT m -1 、80 mT m -1 、90 mT m -1 、100 mT m -1 、200 mT m -1 、300 mT m -1 、400 mT m -1 、500 mT m -1 、600 mT m -1 、700 mT m -1 、800 mT m -1, 900 mTm -1 , 1,000 mTm -1 , or more, up to about 1,000 mTm -1 , 900 mTm -1 , 800 mTm -1 , 700 mTm -1 , 600 mTm -1 , 500 mTm -1 , 400 mTm -1 , 300 mTm -1 , 200 mTm -1 , 100 mTm -1 , 90 mTm -1 , 80 mTm -1 , 70 mTm -1 , 60 mTm -1 , 50 mTm -1 , 40 mTm -1 , 30 mTm -1 , 20 mTm -1 , 10 mTm -1 , 9 mTm -1 , 8 mTm -1 , 7 mTm -1 , 6 mTm -1 , 5 mTm -1 , 4 mTm -1 , 3 mTm -1 , 2 mTm -1 , 1 mTm -1 , 900 μTm -1 , 800 μTm -1 , 700 μTm -1 , 600 μTm -1 , 500 μTm -1 , 400 μTm -1 , 300 μTm -1 , 200 μTm -1 , 100 μTm -1 , 90 μTm -1 , 80 μTm -1 , 70 μTm -1 , 60 μTm -1 , 50 μTm -1 , 40 μTm -1 , 30 μTm -1 , 20 μTm -1 , 10 μTm -1 , 9 μTm -1 , 8 μTm -1 , 7 μTm -1 , 6 μTm-1 , 5 μTm -1 , 4 μTm -1 , 3 μTm -1 , 2 μTm -1 , 1 μTm -1 、or an average magnetic field gradient less than or equal to that (across system 100), or an average magnetic field gradient within a range defined by any two of the foregoing values.

[0094] Method for performing non - classical calculations FIG. 4 shows a flowchart depicting a method 400 for performing non - classical calculations, according to various embodiments. In some embodiments, method 400 is implemented using system 100 of FIG. 1A or FIG. 1B, or system 300 of FIG. 3. At 410, a plurality of dopant molecules contained within at least one host material are obtained. In some embodiments, the plurality of dopant molecules includes any of the dopant molecules described herein with respect to FIG. 1A, FIG. 1B, FIG. 2, or FIG. 3. In some embodiments, the host material includes any of the host materials described herein with respect to FIG. 1A, FIG. 1B, FIG. 2, or FIG. 3. In some embodiments, each dopant molecule is associated with an electronic energy level structure including a triplet electron manifold, as described herein with respect to FIG. 2. In some embodiments, the triplet electron manifold includes a first triplet state, a second triplet state, and a third triplet state, as described herein with respect to FIG. 2.

[0095] In 420, each dopant molecule is configured as a qubit having at least a first qubit state and a second qubit state as described herein with respect to FIGS. 1A, 1B, 2, or 3. In some embodiments, the first qubit state includes a first linear combination of a first triplet state, a second triplet state, and a third triplet state as described herein. In some embodiments, the second qubit state includes a second linear combination of a first triplet state, a second triplet state, and a third triplet state, and the first qubit state is different from the second qubit state as described herein. In some embodiments, the first qubit state or the second qubit state has an arbitrary lifetime as described herein with respect to FIGS. 1A, 1B, 2, or 3 at any temperature as described herein with respect to FIGS. 1A, 1B, 2, or 3. In some embodiments, at least one dopant molecule is coupled to at least one other dopant molecule by an electronic or magnetic dipole coupling interaction having an arbitrary dipole or magnetic coupling strength as described herein with respect to FIGS. 1A, 1B, 2, or 3.

[0096] In 430, non-classical calculations are performed on at least one dopant molecule. In some embodiments, performing a non-classical calculation involves directing a third electromagnetic energy towards at least one dopant molecule, as described herein with respect to FIGS. 1A, 1B, 2, or 3, thereby initializing the quantum state of at least one dopant molecule to a first qubit state or a second qubit state, applying a fourth electromagnetic energy to at least one dopant molecule, thereby performing at least one non-classical operation on at least one dopant molecule, and detecting the electronic state or the nuclear spin state of at least one dopant molecule, thereby obtaining the result of at least one non-classical operation. In some embodiments, the third electromagnetic energy includes any third electromagnetic energy described herein. In some embodiments, the fourth electromagnetic energy includes any fourth electromagnetic energy described herein. In some embodiments, the at least one non-classical operation includes any non-classical operation described herein.

[0097] In some embodiments, performing a non-classical calculation further includes applying a fifth electromagnetic energy and a sixth electromagnetic energy to at least one dopant molecule prior to detecting the nuclear spin state of at least one dopant molecule, as described herein with respect to FIGS. 1A, 1B, 2, or 3. In some embodiments, the fifth electromagnetic energy and the sixth electromagnetic energy, as described herein with respect to FIGS. 1A, 1B, 2, or 3, are jointly configured to transfer information from the electronic state to the nuclear spin state of at least one dopant molecule. In some embodiments, the fifth electromagnetic energy includes any fifth electromagnetic energy described herein. In some embodiments, the sixth electromagnetic energy includes any sixth electromagnetic energy described herein.

[0098] In some embodiments, detecting the electronic state of at least one dopant molecule or the nuclear spin state of at least one dopant molecule includes applying a seventh electromagnetic energy to at least one dopant molecule, as described herein with respect to FIGS. 1A, 1B, 2, or 3, thereby obtaining a result of at least one non-classical operation. In some embodiments, the seventh electromagnetic energy includes any seventh electromagnetic energy described herein. In some embodiments, detecting the electronic state of at least one dopant molecule or the nuclear spin state of at least one dopant molecule further includes detecting light emitted by at least one dopant molecule in response to the seventh electromagnetic energy, as described herein with respect to FIGS. 1A, 1B, 2, or 3.

[0099] Method for generating, manufacturing, or constructing a non-classical computer FIG. 5 shows a flowchart illustrating a method 500 for generating, manufacturing, or constructing a non-classical computer according to various embodiments. In some embodiments, method 500 is used to generate the system 100 of FIG. 1A or FIG. 1B, or the system 300 of FIG. 3. At 510, at least one host material is prepared or obtained. In some embodiments, the at least one host material includes any host material including any host material described herein with respect to FIGS. 1A, 1B, 2, or 3.

[0100] At 520, at least one precursor to at least one dopant molecule is embedded in the at least one host material. For example, in some embodiments, the at least one precursor is embedded in the at least one host material by solution-based growth of a dilute molecular crystal. In some embodiments, the at least one dopant molecule includes any dopant molecule described herein with respect to FIGS. 1A, 1B, 2, or 3. In some embodiments, the at least one precursor includes at least one cleavable moiety. In some embodiments, the at least one cleavable moiety includes any cleavable moiety described herein with respect to FIG. 1A.

[0101] In some embodiments, at least one dopant molecule is associated with an electronic energy level structure that includes a triplet electron manifold, as described herein with respect to FIG. 2. In some embodiments, the triplet electron manifold includes a first triplet state, a second triplet state, and a third triplet state, as described herein with respect to FIG. 2.

[0102] At 530, at least one cleavable portion is cleaved as described herein with respect to FIG. 1A. In some embodiments, cleaving at least one cleavable portion generates at least one dopant molecule and at least one cleaved molecule in at least one host material, as described herein with respect to FIG. 1A. In some embodiments, at least one cleaved molecule includes any cleaved molecule described herein with respect to FIG. 1A. In some embodiments, at least one cleavable portion is cleaved by exposing at least one precursor to light, as described herein with respect to FIG. 1A. In some embodiments, the light includes any light described herein with respect to FIG. 1A.

[0103] Enumeration of Embodiments The foregoing non-limiting embodiments disclosed herein include the following.

[0104] Embodiment 1. A method for generating a non-classical computer, comprising: preparing at least one host material; embedding at least one precursor for at least one dopant molecule into at least one host material, wherein the at least one precursor includes at least one cleavable portion; cleaving at least one cleavable portion, thereby generating at least one dopant molecule and at least one cleaved molecule in at least one host material. At least one dopant molecule includes a qubit having at least a first qubit state and a second qubit state, At least one dopant molecule is associated with an electronic energy level structure including a triplet electron manifold, The triplet electron manifold includes a first triplet state, a second triplet state, and a third triplet state, The first qubit state includes a first linear combination of the first triplet state, the second triplet state, and the third triplet state, The second qubit state includes a second linear combination of the first triplet state, the second triplet state, and the third triplet state, The first qubit state is different from the second qubit state.

[0105] Embodiment 2. The method according to embodiment 1, wherein at least one cleavable portion includes at least one photocleavable portion.

[0106] Embodiment 3. The method according to embodiment 1, wherein at least one photocleavable portion includes at least one diazo, azide, isocyanate, or iodoiminium moiety.

[0107] Embodiment 4. The method according to embodiment 3, wherein at least one cleaved molecule includes at least one dinitrogen molecule, carbon monoxide molecule, or aryl iodide molecule.

[0108] Embodiment 5. The method according to any one of embodiments 1 to 4, wherein cleaving at least one cleavable portion includes exposing at least one precursor to light.

[0109] Embodiment 6. The method according to embodiment 5, wherein the light has a central wavelength of about 200 nanometers (nm) to about 500 nm.

[0110] Embodiment 7. The method according to any one of embodiments 1 to 6, wherein at least one dopant molecule includes a plurality of dopant molecules.

[0111] Embodiment 8. The method according to any one of Embodiments 1 to 7, wherein the host material contains at least one organic molecule.

[0112] Embodiment 9. The method according to any one of Embodiments 1 to 8, wherein the host material contains a crystalline host material, a single-crystalline host material, a polycrystalline host material, a liquid-crystalline host material, a powdered host material, an amorphous host material, or a frozen solution host material.

[0113] Embodiment 10. The host material is a C4-C20 linear or branched alkane; an aromatic hydrocarbon; a polyaromatic hydrocarbon optionally substituted with a methylene, nitrile, carbonyl, carboxylate, alkyl, deuterated alkyl, aryl, deuterated aryl, heteroaryl, deuterated heteroaryl, borane, imine, amine, nitro, phosphine, thioether, ether, fluoro, chloro, bromo, iodo, or thiocarbonyl group; a diaryl ketone; naphthalene; anthracene; pare-terphenyl; benzoic acid; fluorene; biphenyl; benzene; n-hexane; biphenylene; ortho-terphenylen; meta-terphenylen; para-terphenylen; phenanthrene; di(naphthalen-2-yl)methanone; di(phenyl)methanone; or any partial or fully isotopically labeled derivative thereof. The method according to any one of Embodiments 1 to 9.

[0114] Embodiment 11. The method according to any one of Embodiments 1 to 10, wherein the host material contains a thin film having a thickness of at most 100 nanometers (nm).

[0115] Embodiment 12. The method according to any one of Embodiments 1 to 11, wherein at least one dopant molecule contains an organic molecule.

[0116] Embodiment 13. The method according to any one of Embodiments 1 to 12, wherein at least one precursor comprises a derivative of a carbene molecule, a derivative of a nitrene molecule, a diazo derivative of a carbene molecule, an azide derivative of a nitrene molecule, an isocyanate derivative of a nitrene molecule, an imidoiodinane derivative of nitrene, (diazomethylene)dinaphthalene, (diazomethylene)dibenzene, 4-azidobenzoic acid, or any partial or fully isotopically labeled derivative thereof.

[0117] Embodiment 14. The method according to any one of Embodiments 1 to 13, wherein at least one dopant molecule comprises a carbene molecule, a nitrene molecule, a di(naphthalen-2-yl)carbene molecule, a di(phenyl)carbene molecule, or any partial or fully isotopically labeled derivative thereof.

[0118] Embodiment 15. The method according to any one of Embodiments 1 to 14, wherein a plurality of dopant molecules are arranged in a quasi-two-dimensional (quasi-2D) layer.

[0119] Embodiment 16. The method according to Embodiment 15, wherein the quasi-2D layer comprises a self-assembled monolayer (SAM).

[0120] Embodiment 17. The method according to any one of Embodiments 1 to 16, wherein the average distance between dopant molecules is at most 20 nm.

[0121] Embodiment 18. At least one dopant molecule comprises at least 10 3 dopant molecules per cubic micrometer (μm 6 ) and is contained in at least one host material, according to the method of any one of Embodiments 1 to 17.

[0122] Embodiment 19. At least one dopant molecule comprises a plurality of dopant molecules, A first dopant molecule among a plurality of dopant molecules is configured to absorb first electromagnetic energy having a first central wavelength or a first central frequency, A second dopant molecule among the plurality of dopant molecules is configured to absorb second electromagnetic energy having a second central wavelength or a second central frequency, The method according to any one of Embodiments 1 to 18, wherein the first central wavelength or the first central frequency is different from the second central wavelength or the second central frequency.

[0123] Embodiment 20. The first central wavelength or the first central frequency is associated with a first wavelength range or a first frequency range having a first full width at half maximum (FWHM) bandwidth, The second central wavelength or the second central frequency is associated with a second wavelength range or a second frequency range having a second FWHM bandwidth, The method according to Embodiment 19, wherein the first wavelength range or the first frequency range within the first FWHM bandwidth and the second wavelength range or the second frequency range within the second FWHM bandwidth do not overlap.

[0124] Embodiment 21. The method according to Embodiment 20, wherein the first FWHM bandwidth or the second FWHM bandwidth is at most 100 megahertz (MHz).

[0125] Embodiment 22. The method according to any one of Embodiments 19 to 21, wherein the first central wavelength or the second central wavelength is 200 nm to 1,000 nm.

[0126] Embodiment 23. The method according to Embodiment 21, wherein the first FWHM bandwidth or the second FWHM bandwidth is at most 100 gigahertz (GHz).

[0127] Embodiment 24. The method according to Embodiment 23, wherein the first central frequency or the second central frequency is 1 MHz to 100 GHz.

[0128] Embodiment 25. The method according to any one of Embodiments 1 to 24, wherein the triplet electronic manifold includes the ground state triplet (GST) electronic manifold.

[0129] Embodiment 26. A system for performing non-classical calculations, at least one host material, at least one dopant molecule contained in the at least one host material, at least one cleaved molecule contained in the at least one host material, comprising: at least one dopant molecule includes a qubit having at least a first qubit state and a second qubit state, at least one dopant molecule is associated with an electronic energy level structure including a triplet electronic manifold, the triplet electronic manifold includes a first triplet state, a second triplet state, and a third triplet state, the first qubit state includes a first linear combination of the first triplet state, the second triplet state, and the third triplet state, the second qubit state includes a second linear combination of the first triplet state, the second triplet state, and the third triplet state, the first qubit state is different from the second qubit state, a system.

[0130] Embodiment 27. The system according to Embodiment 26, wherein at least one dopant molecule and at least one cleaved molecule are generated by cleaving at least one precursor to at least one dopant molecule, and at least one precursor includes at least one cleavable moiety.

[0131] Embodiment 28. The system according to Embodiment 27, wherein at least one cleavable moiety includes at least one photo-cleavable moiety.

[0132] Embodiment 29. The system according to Embodiment 28, wherein at least one photo-cleavable moiety comprises at least one diazo moiety, azide moiety, isocyanate moiety, or iodoiminium moiety.

[0133] Embodiment 30. The system according to Embodiment 29, wherein the cleaved molecule comprises at least one dinitrogen molecule, carbon monoxide molecule, or aryl iodide molecule.

[0134] Embodiment 31. The system according to any one of Embodiments 27 to 30, wherein cleaving at least one precursor comprises exposing at least one precursor to light.

[0135] Embodiment 32. The system according to Embodiment 31, wherein the light has a central wavelength of about 200 nanometers (nm) to about 500 nm.

[0136] Embodiment 33. The system according to any one of Embodiments 26 to 32, wherein at least one dopant molecule comprises a plurality of dopant molecules.

[0137] Embodiment 34. The system according to any one of Embodiments 26 to 33, wherein the host material comprises at least one organic molecule.

[0138] Embodiment 35. The system according to any one of Embodiments 26 to 34, wherein the host material comprises a crystalline host material, single-crystalline host material, polycrystalline host material, liquid-crystalline host material, powdered host material, amorphous host material, or frozen solution host material.

[0139] Embodiment 36. The system according to any one of Embodiments 26 to 35, wherein the host material comprises a C4-C20 linear or branched alkane; an aromatic hydrocarbon; a polyaromatic hydrocarbon optionally substituted with a methylene, nitrile, carbonyl, carboxylate, alkyl, deuterated alkyl, aryl, deuterated aryl, heteroaryl, deuterated heteroaryl, borane, imine, amine, nitro, phosphine, thioether, ether, fluoro, chloro, bromo, iodo, or thiocarbonyl group; a diaryl ketone; naphthalene; anthracene; para-terphenyl; benzoic acid; fluorene; biphenyl; benzene; n-hexane; biphenylene; ortho-terphenylen; meta-terphenylen; para-terphenyl; phenanthrene; di(naphthalen-2-yl)methanone; di(phenyl)methanone; or any partial or fully isotopically labeled derivative thereof.

[0140] Embodiment 37. The system according to any one of Embodiments 26 to 36, wherein the host material comprises a thin film having a thickness of up to 100 nanometers (nm).

[0141] Embodiment 38. The system according to any one of Embodiments 26 to 37, wherein at least one dopant molecule comprises an organic molecule.

[0142] Embodiment 39. The system according to any one of Embodiments 26 to 38, wherein at least one precursor comprises a derivative of a carbene molecule, a derivative of a nitrene molecule, a diazo derivative of a carbene molecule, an azide derivative of a nitrene molecule, an isocyanate derivative of a nitrene molecule, an imidoyodine derivative of a nitrene molecule, (diazomethylidene)dinaphthalene, (diazomethylidene)dibenzene, 4-azidobenzoic acid, or any partial or fully isotopically labeled derivative thereof.

[0143] Embodiment 40. The system according to any one of Embodiments 26 to 39, wherein at least one dopant molecule includes a carbene molecule, a nitrene molecule, a di(naphthalen-2-yl)carbene molecule, a di(phenyl)carbene molecule, or any partially or fully isotopically labeled derivative thereof.

[0144] Embodiment 41. The system according to any one of Embodiments 26 to 40, wherein a plurality of dopant molecules are arranged in a quasi-two-dimensional (quasi-2D) layer.

[0145] Embodiment 42. The system according to Embodiment 41, wherein the quasi-2D layer includes a self-assembled monolayer (SAM).

[0146] Embodiment 43. The system according to any one of Embodiments 26 to 42, wherein the average distance between dopant molecules is at most 20 nm.

[0147] Embodiment 44. At least one dopant molecule is contained in at least one host material at a concentration of at least 10 dopant molecules per cubic micrometer (μm 3 ) of the system according to any one of Embodiments 26 to 43. 6

[0148] Embodiment 45. At least one dopant molecule includes a plurality of dopant molecules, a first dopant molecule among the plurality of dopant molecules is configured to absorb first electromagnetic energy having a first central wavelength or a first central frequency, a second dopant molecule among the plurality of dopant molecules is configured to absorb second electromagnetic energy having a second central wavelength or a second central frequency, and the first central wavelength or the first central frequency is different from the second central wavelength or the second central frequency, the system according to any one of Embodiments 26 to 44.

[0149] Embodiment 46. The first central wavelength or the first central frequency is associated with a first wavelength range or a first frequency range having a first full width at half maximum (FWHM) bandwidth, The second central wavelength or the second central frequency is associated with a second wavelength range or a second frequency range having a second FWHM bandwidth, The system according to embodiment 45, wherein the first wavelength range or the first frequency range within the first FWHM bandwidth and the second wavelength range or the second frequency range within the second FWHM bandwidth do not overlap.

[0150] Embodiment 47. The system according to embodiment 46, wherein the first FWHM bandwidth or the second FWHM bandwidth is at most 100 megahertz (MHz).

[0151] Embodiment 48. The system according to any one of embodiments 45 to 47, wherein the first central wavelength or the second central wavelength is in the range of 200 nm to 1,000 nm.

[0152] Embodiment 49. The system according to embodiment 48, wherein the first FWHM bandwidth or the second FWHM bandwidth is at most 100 gigahertz (GHz).

[0153] Embodiment 50. The system according to embodiment 49, wherein the first central frequency or the second central frequency is in the range of 1 MHz to 100 GHz.

[0154] Embodiment 51. The system according to any one of embodiments 26 to 50, wherein the triplet electron manifold includes a ground state triplet (GST) electron manifold.

[0155] Embodiment 52. The system according to any one of embodiments 26 to 51, further comprising at least one initialization unit configured to direct a third electromagnetic energy towards at least one dopant molecule, thereby initializing the quantum state of the at least one dopant molecule to a first qubit state or a second qubit state.

[0156] Embodiment 53. The system according to Embodiment 52, wherein the third electromagnetic energy includes at least one wavelength in the range of 200 nm to 1,000 nm.

[0157] Embodiment 54. The system according to any one of Embodiments 26 to 53, further comprising at least one non-classical operation unit configured to apply fourth electromagnetic energy to at least one dopant molecule, thereby performing at least one non-classical operation on the at least one dopant molecule.

[0158] Embodiment 55. The system according to Embodiment 54, wherein the at least one non-classical operation includes at least one quantum operation, at least one quantum computing operation, at least one quantum gate operation, at least one quantum simulation operation, or at least one quantum annealing operation.

[0159] Embodiment 56. The system according to Embodiment 54 or 55, wherein the fourth electromagnetic energy includes at least one frequency in the range of 1 MHz to 100 GHz.

[0160] Embodiment 57. The system according to any one of Embodiments 54 to 56, wherein after performing the at least one non-classical operation, the result of the at least one non-classical operation correlates with the electronic state of the at least one dopant molecule.

[0161] Embodiment 58. The system according to Embodiment 57, further comprising at least one storage unit configured to apply fifth electromagnetic energy and sixth electromagnetic energy to at least one dopant molecule, and the fifth electromagnetic energy and the sixth electromagnetic energy are jointly configured to transfer information from the electronic state of the at least one dopant molecule to the nuclear spin state.

[0162] Embodiment 59. The system according to Embodiment 58, wherein the fifth electromagnetic energy and the sixth electromagnetic energy jointly apply a swap gate to at least one dopant molecule, thereby transmitting information from the electronic state to the nuclear spin state of the at least one dopant molecule.

[0163] Embodiment 60. The system according to Embodiment 58 or 59, wherein the fifth electromagnetic energy includes at least one frequency from 1 kHz to 100 MHz, and the sixth electromagnetic energy includes at least one frequency from 1 MHz to 100 GHz.

[0164] Embodiment 61. The system according to any one of Embodiments 26 to 60, further comprising at least one detection unit configured to detect the electronic state of at least one dopant molecule or the nuclear spin state of at least one dopant molecule, thereby obtaining the result of at least one non-classical operation.

[0165] Embodiment 62. The system according to Embodiment 61, wherein at least one detection unit is configured to apply a seventh electromagnetic energy to at least one dopant molecule, thereby obtaining the result of at least one non-classical operation.

[0166] Embodiment 63. The system according to Embodiment 61 or 62, wherein at least one detection unit includes at least one optical detector configured to detect light emitted by at least one dopant molecule in response to the seventh electromagnetic energy.

[0167] Embodiment 64. The system according to Embodiment 63, wherein the light emitted by at least one dopant molecule has a first optical property associated with a first qubit state and a second optical property associated with a second qubit state, and the first optical property is different from the second optical property.

[0168] Embodiment 65. The system according to embodiment 64, wherein the first optical property or the second optical property includes light intensity, polarization, wavelength, or frequency.

[0169] Embodiment 66. The system according to any one of embodiments 26 to 65, further comprising a cryogenic unit configured to include at least one host material and cool the at least one host material to a temperature of up to 20K.

[0170] Embodiment 67. The system according to embodiment 66, wherein the cryogenic unit includes a helium cryocooler or a closed-cycle helium cryocooler.

Examples

[0171] Example 1: General synthesis and characterization procedures Unless otherwise stated, commercially available materials were used without purification. Moisture- and oxygen-sensitive reactions were carried out in flame-dried glassware and under an inert atmosphere of purified argon using syringe / septum techniques. Thin-layer chromatography (TLC) was performed on aluminum plates coated with silica gel 60 F 254 with a thickness of 0.20 mm. The developed plates were visualized using ultraviolet (UV) light at wavelengths of 254 nm and 365 nm. NMR spectra were recorded on a Bruker Avance Neo 400 MHz or Bruker Avance Neo 600 MHz spectrometer operating at 400.13 MHz for 1 1H, 13 100.61 MHz for 1 13C, or 13 600.15 MHz for 1 1H, and 13 150.94 MHz for 1 13C. NMR chemical shifts (δ) are reported in parts per million (ppm). 13 For the 1313C NMR spectra were recorded in proton decoupling mode. Coupling constants (J) are given in Hz and apparent resonance multiplicities are reported as s (singlet), d (doublet), t (triplet), q (quartet), quint (quintet), or m (multiplet). Flash chromatography was performed using a Biotage® Sfär HC Duo column as the stationary phase with a Biotage® Selekt Flash Purification System. Electron paramagnetic resonance (EPR) spectra were recorded on an X-band EPR spectrometer (Bruker ELEXSYS E580) using software xEPR for data acquisition. Measurements were carried out using a dielectric ring resonator (Bruker model 4118X-MD5, typical microwave frequency ~9.7 GHz) mounted in a helium flow cryostat (Oxford CF935) with optical access. When operating in continuous wave (cw) mode, a typical quality factor of about 10,000 was achieved and typical modulation amplitudes and frequencies were 1 gauss (G) and 100 kHz, respectively. In the pulsed mode, an arbitrary waveform generator of Bruker SpinJet with a 1 kW traveling wave tube (TWT) amplifier (Applied Systems Engineering model 117) was used. Prior to measurement, the sample was inserted into an EPR tubular (Wilmad quartz CFQ) with an outer diameter (OD) of 4 millimeters (mm) and aligned at a homemade Teflon® sample stage. The sample can be rotated on a uniaxial goniometer stage (Bruker E218G1).

[0172] Example 2: General synthetic route for the formation of carbene dopant molecules A general synthetic route for the formation of carbene dopant molecules in an organic host material is shown below. [Chemical formula]

[0173] Carbenes are designed to have a triplet ground state in which two unpaired electrons are close and restricted by molecular orbitals. As a result, the electron coupling is maximized, and the zero-field splitting parameters D and E of the electron spin are large. Furthermore, the spin-lattice relaxation time benefits from the weak spin-orbit coupling typically present in pure organic materials. Carbenes can be included in a cyclic structure (1) and can be substituted by one or more nitrile groups, carbonyl groups, carboxylic acid groups, ester groups, alkyl groups, aryl groups, heteroaryl groups, amine groups, nitro groups, phosphine groups, alcohol groups, ether groups, thioether groups, or halogen groups at two (2) or one (3) aryl or heteroaryl groups π 1-3 and may be included. Such groups can be selected (e.g., using computational molecular modeling, high-throughput synthesis and screening, etc.) to finely tune electronic properties such as ZFS, zero-phonon lines, spectral stability, and / or thermodynamic / kinetic stability.

[0174] Since carbenes are typically not stable enough to directly prepare dilute molecular crystals, stable carbene precursors are instead embedded in a molecular matrix (compounds 4 - 6) and then activated (i.e., converted from the carbene precursor form to the activated carbene form). Carbene precursors typically contain a diaryldiazo group (R2C=N- - =N), which can be photoactivated with light (λ = 200 - 500 nm) to generate molecules of dinitrogen N2 and carbene molecules. Examples of such activation are shown below.

Chemical Structure

[0175] The host materials (Compounds 6 - 9) in which the carbene is embedded are typically structurally similar to the carbene precursors 1 - 3 respectively, and are designed to enable the formation of dilute molecular crystals by substitution of the host material (i.e., the matrix) molecules with the carbene precursor. This isostructural relationship enables the preparation of high-quality dilute molecular crystals by reducing the amount of strain imparted by the dopant molecule (i.e., the carbene). Both the carbene and the host material can be partially or fully deuterated to reduce the magnetic noise of the dilute molecular crystal and thus enhance the spin - spin coherence time T2. Using bottom - up synthetic chemistry, the molecules can also be 13 selectively labeled at C (e.g., at the carbene carbon), adding nuclear spin manifolds that can be used for quantum state preparation. Packing the molecules closely in a molecular - on arrangement serves to trap inert N2 molecules in close proximity to the reactive carbene centers, thereby shielding it from any nearby reaction partners and stabilizing the carbene.

[0176] Example 3: Synthesis of the compounds required to embed di(naphthalen - 2 - yl)carbene in di(naphthalen - 2 - yl)methanone The synthetic route for the formation of di(naphthalen - 2 - yl)carbene dopant molecules in the di(naphthalen - 2 - yl)methanone host material is shown below.

Chemical formula

[0177] a) Formation of di(naphthalen - 2 - yl)methanone

Chemical formula

[0178] b) Formation of (di(naphthalen - 2 - yl)methylene)hydrazine

Chemical formula

[0179] c) Formation of 2,2'-(diazomethylene)dinaphthalene JPEG2025519028000010.jpg140150

[0180] d) Formation of dilute molecular crystals of 2,2'-(diazomethylene)dinaphthalene in di(naphthalen-2-yl)methanone Di(naphthalen-2-yl)methanone (0.85 grams) was dissolved in hot ethyl acetate (HPLC grade, 100 mL, 0.030 M), and the solution was cooled to room temperature. In the dark, 2,2'-(diazomethylene)dinaphthalene (0.91 milligrams, 1025 ppm) was added to this solution. An aliquot (5 milliliters, mL) of this resulting parent solution was added to a 10 mL vial using a syringe equipped with a 0.45 μm pore size syringe filter, and the vial was placed in a screw-top jar filled with ethanol (HPLC grade). The molecular crystals (parallelepiped approximately 5×4×4 mm) formed while storing in the dark at room temperature for 7 days were diluted. The crystals were isolated in the dark, washed with ethanol (HPLC grade), and dried in vacuo. The dilute molecular crystals can be stored in the dark in a freezer (T = -22 °C) for several months without detectable decomposition.

[0181] To generate di(naphthalen-2-yl)carbene dopant molecules in the di(naphthalen-2-yl)methanone host material, the dilute molecular crystals of 2,2'-(diazomethylene)dinaphthalene in di(naphthalen-2-yl)methanone need only be exposed to light of the correct wavelength, as described herein.

[0182] Example 4: Synthesis of the compounds necessary to embed diphenylcarbene in diphenylmethane The synthetic route for the formation of diphenylcarbene dopant molecules in the diphenylmethane host material is shown below.

Chemical formula

[0183] a) Formation of (diphenylmethylene)hydrazine

Chem.

[0184] b) Formation of (diazomethylidene)dibenzene

Chem.

[0185] c) Formation of dilute molecular crystals of (diazomethylidene)dibenzene in di(phenyl)methanone Di(phenyl)methanone (0.30 g, purified by sublimation) was dissolved in hot n-hexane (HPLC grade, 4.1 mL, 0.40 M), and the solution was cooled to room temperature. In the dark, (diazomethylidene)dibenzene (0.08 mg, 247 ppm) was added to this solution. An aliquot (1.0 mL, mL) of this resulting parent solution was added to a 3.0 mL vial, which was sealed via a pierced screw cap. The molecular crystals (ca. 6 × 4 × 3 mm) formed upon storage in the dark at room temperature for 6 days were diluted. The crystals were isolated in the dark, washed with cold n-hexane (HPLC grade), and dried in vacuo. The dilute molecular crystals can be stored in the dark in a freezer (T = -22 °C) for several months without detectable decomposition.

[0186] To generate di(phenyl)carbene dopant molecules in the di(phenyl)methanone host material, the dilute molecular crystals of (diazomethylidene)dibenzene in di(phenyl)methanone need only be exposed to light of the correct wavelength, as described herein.

[0187] Example 5: Di(naphthalen-2-yl)carbene-d 14 Synthesis of the compounds necessary for embedding into di(naphthalen-2-yl)methanone-d 14 Di(naphthalen-2-yl)methanone-d 14 Di(naphthalen-2-yl)carbene-d in the host material 14 The synthetic route for the formation of the dopant molecule is shown below.

Chemical formula

[0188] a) Formation of di(naphthalen-2-yl)methane

Chemical formula

[0189] b) Formation of di(naphthalen-2-yl)methane-d 14

Chemical formula

[0190] c) Formation of di(naphthalen-2-yl)methanone-d 14

Chemical formula

[0191] d) Formation of (di(naphthalen-2-yl)methylene)hydrazine-d 14

Chemical formula

[0192] e) Formation of 2,2'-(diazomethylene)dinaphthalene-d 14

Chemical formula

[0193] f) Di(naphthalen-2-yl)methanone-d 14 2,2'-(Diazomethylene)dinaphthalene-d in 14 formation of dilute molecular crystals of Di(naphthalen-2-yl)methanone-d 14 (0.80 grams) was dissolved in hot ethyl acetate (HPLC grade, 90 mL, 0.030 M), and the solution was cooled to room temperature. In the dark, to this solution, 2,2'-(diazomethylene)dinaphthalene-d 14 (4.5 milligrams, 5400 ppm) was added. An aliquot (5 milliliters, mL) of this resulting parent solution was added to a 10 mL vial using a syringe equipped with a 0.45 μm pore size syringe filter, and the vial was placed in a screw-top jar filled with ethanol (HPLC grade). The molecular crystals (parallelepiped approximately 3×3×4 mm) formed while storing at room temperature for 7 days in the dark were diluted. The crystals were isolated in the dark, washed with ethanol (HPLC grade), and dried in vacuo. The dilute molecular crystals can be stored for several months in the dark in a freezer (T = -22 °C) without detectable decomposition.

[0194] Di(naphthalen-2-yl)methanone-d 14 Di(naphthalen-2-yl)carbene-d in the host material 14 To generate the dopant molecule, Di(naphthalen-2-yl)methanone-d 14 2,2'-(Diazomethylene)dinaphthalene-d in 14 the dilute molecular crystals of need only be exposed to light of the correct wavelength, as described herein.

[0195] Example 6: Di(phenyl)carbene-d 10 Synthesis of the compounds necessary to embed into Di(phenyl)methanone-d 10 Di(phenyl)methanone-d 10 Di(phenyl)carbene-d in the host material 10 The synthetic route for the formation of the dopant molecule is shown below. [Chemistry]

[0196] a) Di(phenyl)methanone-d 10 Formation [Chemistry]

[0197] b) (Di(phenyl)methylene)hydrazine-d 10 Formation [Chemistry] (Di(phenyl)methylene)hydrazine-d 10 was prepared by modifying the procedure described in E. Schmitt, G. Landelle, J.-P. Vors, N. Lui, S. Pazenok, F. R. Leroux, Eur. J. Org. Chem. 2015, 2015, 6052.

[0198] JPEG2025519028000023.jpg82150

[0199] c) (Diazomethylene)dibenzene-d 10 Formation [Chemistry]

[0200] d) Di(phenyl)methanone-d 10 in (Diazomethylene)dibenzene-d 10 Formation of dilute molecular crystals Di(phenyl)methanone-d 10 (0.30 grams, purified by sublimation) was dissolved in hot n-pentane (HPLC grade, 7.8 milliliters, 0.20 M), and the solution was cooled to room temperature. In the dark, (Diazomethylene)dibenzene-d 10(0.08 mg, 247 ppm) was added. An aliquot (1.0 milliliter, mL) of this resulting parent solution was added to a 3.0 mL vial and sealed with a pierced screw cap. The molecular crystals (approx. 3×5×4 mm) formed during storage at 7 °C for 12 days in the dark were diluted. The crystals were isolated in the dark, washed with cold n-pentane (HPLC grade), and dried in vacuo. The diluted molecular crystals can be stored for several months in the dark in a freezer (T = -22 °C) without detectable decomposition.

[0201] Di(phenyl)methane-d 10 Di(phenyl)carbene-d in the host material 10 To generate the dopant molecule, di(phenyl)methane-d 10 1,1'-(diazomethylene)dibenzene-d in 10 The diluted molecular crystals thereof need only be exposed to light of the correct wavelength, as described herein.

[0202] Example 7: Di(naphthalen-2-yl)carbene- 13 C-d 14 Embedded in di(naphthalen-2-yl)methane- 13 C-d 14 Synthesis of the compounds required for Di(naphthalen-2-yl)methane- 13 C-d 14 Di(naphthalen-2-yl)carbene- in the host material 13 C-d 14 The synthetic route for the formation of the dopant molecule is shown below.

Chemical formula

[0203] a) Formation of 2-bromonaphthalene-d7

Chemical formula

[0204] b) Formation of 2-naphthoic acid- 13 C-d7 [Chemical formula]

[0205] c) N-Methoxy-N-methyl-2-naphthamide- 13 Formation of C-d7 [Chemical formula]

[0206] d) Di(naphthalen-2-yl)methanone- 13 C-d 14 Formation [Chemical formula]

[0207] e) (Di(naphthalen-2-yl)methylene- 13 C) hydrazine-d 14 Formation [Chemical formula]

[0208] f) 2,2'-(Diazomethylene- 13 C) dinaphthalene-d 14 Formation [Chemical formula]

[0209] g) Di(naphthalen-2-yl)methanone- 13 C-d 14 in (Diazomethylene)dinaphthalene- 13 C-d 14 Formation of dilute molecular crystals Di(naphthalen-2-yl)methanone- 13 C-d 14 (0.80 grams) was dissolved in hot ethyl acetate (HPLC grade, 90 mL, 0.030 M), and the solution was cooled to room temperature. In the dark, to this solution was added 2,2'-(Diazomethylene)dinaphthalene- 13 C-d14 (4.5 milligrams, 5400 ppm) was added. An aliquot (5 milliliters, mL) of this resulting parent solution was added to a 10 mL vial using a syringe equipped with a 0.45 μm pore size syringe filter, and the vial was placed in a screw-top jar filled with ethanol (HPLC grade). Dilute the molecular crystals (parallelepiped approximately 3×3×4 mm) formed while storing in the dark at room temperature for 7 days. Isolate the crystals in the dark, wash with ethanol (HPLC grade), and dry in vacuo. The diluted molecular crystals can be stored in the dark in a freezer (T = -22 °C) for several months without detectable decomposition.

[0210] Di(naphthalen-2-yl)methanone- 13 C-d 14 Di(naphthalen-2-yl)carbene- in the host material 13 C-d 14 To generate the dopant molecule, di(naphthalen-2-yl)methanone- 13 C-d 14 (Diazomethylene)dinaphthalene in 13 C-d 14 The diluted molecules of are only required to be exposed to light of the correct wavelength, as described herein.

[0211] Example 8: X-ray Crystal Structure of (Diazomethylene)dinaphthalene Embedded in Di(naphthalen-2-yl)methanone Dilute single crystals of 2,2'-(diazomethylene)dinaphthalene embedded in di(naphthalen-2-yl)methanone were grown within 7 days at room temperature by slow vapor diffusion of a dilute solution of 2,2'-(diazomethylene)dinaphthalene (340 ppm) and di(naphthalen-2-yl)methanone (0.035 M) in ethyl acetate, excluding light. Select suitable crystals, Cu-K αRadiation with λ = 1.54178 Å was used with an Atlas diffractometer mounted on a SuperNova, Dual, Cu. The crystal was maintained at 150.00(14) Kelvin during data collection. Using Olex2, the structure was solved with the XT structure solution program using intrinsic phasing and refined with the XL refinement package using least-squares minimization. All non-H atoms were refined with anisotropic thermal parameters. H atoms in all structures were refined at calculated positions in a rigid group model. Table 1 shows the obtained crystal data. Due to the nature of the diffraction measurements, only periodically assembled molecules (i.e., the host material) appear in the crystal structure, and the carbene precursor is not observed.

Table 1

[0212] Example 9: General Synthetic Route for the Formation of Nitrene Dopant Molecules A general synthetic route for the formation of nitrene dopant molecules in an organic host material is shown below.

Chemical formula

[0213] The nitrene material is prepared according to the same principle as outlined above for the preparation of the carbene. That is, the photoactive nitrene precursor is embedded in an inert matrix (i.e., the host material) by substitution doping, and the activated nitrene 10 is obtained after photolysis using an appropriate light source. The nitrene can be directly linked to an aryl group or can be linked via a sulfonyl group (-SO2-) linker. The substituents of the nitrene aryl unit can be used to finely tune the thermodynamic / kinetic stability and electronic properties. Here too, one or more substituents R can have one or more nitrile groups, carbonyl groups, carboxylic acid groups, ester groups, alkyl groups, aryl groups, heteroaryl groups, imine groups, amine groups, nitro groups, phosphine groups, alcohol groups, ether groups, thiol groups, thioether groups, or halogen groups bonded thereto. Similar to the case of the carbene, such groups can be selected (e.g., using computational molecular modeling, high-throughput synthesis and screening, etc.) to finely tune electronic properties such as ZFS, zero phonon lines, spectral stability, and / or thermodynamic / kinetic stability.

[0214] The precursors of nitrene (10) are aryl azide (-N3, 11), aryl isocyanate (-NCO, 12), or iminoyodine (13). Each of these groups can be photolyzed with UV / vis light (λ = 200 - 500 nm) to obtain molecules of nitrene and dinitrogen N2, carbon monoxide CO, or aryl iodide, respectively.

Chemical formula

[0215] An exemplary route for embedding the aryl azide precursor (15) in a structurally related matrix (16) is shown below.

Chemical formula

[0216] Example 10: Formation of dilute molecular crystals of 4-azidobenzoic acid in 4-iodobenzoic acid 4-Iodobenzoic acid (1.00 gram) was dissolved in methanol (HPLC grade, 50 mL, 0.080 M), and the solution was cooled to room temperature. In the dark, to this solution was added 4-azidobenzoic acid (0.2 M in tert-butyl methyl ether, ≧95.0%, 130 μL, 6600 ppm). An aliquot (8 milliliters, mL) of the resulting parent solution was added to a 10 mL vial using a syringe equipped with a 0.20 μm pore size syringe filter, and the vial was stored in the dark at room temperature for 4 days. Dilute molecular crystals (thin rectangular plates of about 5×10×0.01 mm) were isolated in the dark, washed with a small amount of cold methanol (HPLC grade), and dried in vacuo.

[0217] To generate 4-nitrene benzoic acid dopant molecules in the 4-iodobenzoic acid host material, the dilute molecular crystals of 4-azidobenzoic acid in 4-iodobenzoic acid need only be exposed to light of the correct wavelength, as described herein.

[0218] Example 11: Optical Crystal Alignment for Characterization of Dopant Molecules in a Host Material A chemical system created by embedding a dopant molecule (or its precursor) into a host material may also be referred to herein as a “dilute molecular crystal”. Dilute molecular crystals exhibit intrinsic birefringence, i.e., they are optically anisotropic. This property can be used to identify a set of axes of the material (i.e., an orthogonal axis system of the optical index ellipsoid axes n1, n2, and n3) for later alignment in an experimental setup. Such axes can be identified using a transmission mode microscope with two crossed linear polarizers (shown as a polarizer and an analyzer).

[0219] Here, an example of a typical configuration when the crystal is rotated within the field of view is given. Each time the crossed polarizer axes are parallel to the vectors n1 and n2 (or more generally, to their projections in a plane perpendicular to the viewing direction), the crystal appears dark, and when the crystal is positioned in any other orientation, some light passes through the analyzer and the crystal displays a variable degree of brightness. The maximum brightness of the birefringent material is observed when the polarizer axis and the analyzer axis are at an angle of 45° with respect to n1 and n2. Using this method, the crystal can also be examined for microscopic defects such as strain-induced elongation effects (e.g., edge or screw dislocations).

[0220] Example 12: Preparation, Photoactivation, and Annealing of Carbene in a Host Material After the crystal index ellipsoid has been macroscopically determined via the optical alignment method described above, crystals of a suitable size are prepared via micro-mechanical methods (e.g., doctor blade cutting, diamond wire saw, etc.) from the as-grown crystals, and, if necessary, the surface is cut or polished with a suitable organic solvent (e.g., hexane, pentane, ethanol, methanol). The prepared crystals are transferred to a suitable sample holder (e.g., an electron paramagnetic resonance (EPR) tube, a glass sample holder, etc.) and placed into the device of interest (e.g., EPR, optical instrument) using an integrated cryostat. The sample is cooled to a temperature at which the generated carbene or nitrene is stable (depending on the carbene or nitrene itself and the matrix). Using an integrated optical access such as an optical fiber or a window, the sample is irradiated with light (e.g., a UV LED in the wavelength range of 300 - 400 nm) in a macroscopic manner for a certain period of time (depending on the light source output power, from seconds to hours) to activate the entire sample. This process involves the conversion of carbene or nitrene precursor molecules embedded in a suitable matrix to their corresponding carbene and one nitrogen molecule (also possible for nitrene, carbon monoxide, and aryl iodide). Alternatively, a focused laser beam that can be adjusted in the lateral dimensions (x-axis and y-axis) can be used to activate regions of carbene or nitrene with dimensions > 200 nm.

[0221] Figure 6A shows exemplary continuous wave (cw) EPR signals associated with the stepwise photoactivation of di(naphthalen-2-yl)carbene (500 ppm) in di(naphthalen-2-yl)methane at a temperature of 25 K using a green laser (λ = 532 nm). The appearance of the ground state triplet carbene can be seen. Figure 6B shows the double integral of the cw EPR signal from Figure 6A as a function of the applied optical energy and shows the activation process for obtaining activated carbene in a dilute molecular crystal. Such plots can be used as calibration curves for activating dopant molecules (e.g., carbene dopant molecules) in a dilute molecular crystal. By using such calibration curves (i.e., the amount of carbene activated per irradiation time), carbene with a well-defined density can be generated within the doped molecular crystal. A lithography method can be used to write the pattern of qubits onto the sample (e.g., gradients, connection regions, lattices).

[0222] At very low temperatures (in some cases < 140 K, for other samples < 260 K), the carbene and dinitrogen molecules are kinetically trapped within the matrix such that they cannot adopt the molecular shape typical of carbene. An annealing procedure involving controllably heating the sample to a sample-dependent temperature (here 140 K, > 50 K for other samples) for a sufficient time (minutes to hours) induces the reorientation of the activated carbene and their direct molecular environment within the dilute molecular crystal. The process can be monitored by cw EPR.

[0223] Figure 7A shows exemplary cw EPR signals associated with the conversion of newly photoactivated di(naphthalen-2-yl)carbene (340 ppm) in di(naphthalen-2-yl)methanone to the annealed form at a temperature of 140 K. The annealing process is observed as the disappearance of the cw EPR signal at 6925 G and the appearance of a new signal at 7065 G. Figure 7B shows the double integral of the cw EPR signal from Figure 7A as a function of the annealing time. The process typically involves line sharpening and can thus be used to further control the inhomogeneous broadening within the sample necessary for efficient single-molecule manipulation via optical control. Figure 7B shows the appearance and disappearance of the annealed and non-annealed signals, respectively, at a particular point in time.

[0224] Example 13: Di(naphthalen-2-yl)methanone-d 14 Di(naphthalen-2-yl)carbene-d in 14 Spin-lattice (T1) and spin-spin (T2) relaxation times of The spin-lattice (T1) relaxation time was measured for a sample of di(naphthalen-2-yl)carbene-d (5400 ppm) in di(naphthalen-2-yl)methanone-d at 466.6 mT, and the magnetic field was approximately parallel to one of the principal axes of the zero-field splitting tensor 14 Di(naphthalen-2-yl)carbene-d in 14 (5400 ppm), and the magnetic field was approximately parallel to one of the principal axes of the zero-field splitting tensor

Number

Number

[0225] The spin-spin (T2) relaxation time was measured using a Hahn acoustic pulse sequence (π / 2-τ-π-τ-echo) and fitted to a stretched exponential decay similar to the above-described procedure. The measured values used a rectangular 10 ns π / 2 pulse and a 20 ns π pulse and a 4-step phase cycle. FIG. 9 shows the decay curves of protonated and deuterated diluted molecular crystals, highlighting a significant increase in T2 due to the perdeuteration of the diluted molecular crystals. As an example, for a protonated sample ((di(naphthalen-2-yl)carbene (5400 ppm) in di(naphthalen-2-yl)methane), the most likely T 2、max of 4.78 μs and an average T 2、av of 2.67 μs were observed, while the perdeuterated sample of di(naphthalen-2-yl)carbene-d 14 in di(naphthalen-2-yl)methane-d 14 (5400 ppm) gave a most likely T 2、max of 53.6 μs and an average T 2、av of 16.0 μs. It should be noted that the distortion of the line shape of these spectra can occur due to inhomogeneous broadening and electron spin echo envelope modulation (ESEEM) effects arising from the bonds to hydrogen and deuterium nuclei near the electron spin, respectively.

[0226] Example 14: Intermolecular Binding Strength of Di(naphthalen-2-yl)carbene-d 14 in Di(naphthalen-2-yl)methane-d 14 A double electron-electron resonance (DEER) experiment was carried out to probe the intermolecular bonds between randomly distributed carbenes in a diluted molecular crystal. An echo-detected electric field sweep spectrum was collected using a Hahn echo pulse sequence with a fixed τ value while sweeping the magnetic field. To selectively address the probe pulse and the pump pulse in the DEER experiment, 13 a large coupling of 214.6 MHz observed for the crystal orientation due to the hyperfine coupling (HFC) with the C carbene carbon

Number

[0227] Example 15: Preparation, Photoactivation, and Annealing of Nitrenes in a Host Material Figure 11A shows exemplary continuous wave (cw) EPR signals associated with the stepwise photoactivation of 4-nitrenebenzoic acid in 4-iodobenzoic acid at a temperature of 25 K using light of a wavelength of λ = 370 nm. The appearance of the ground state triplet nitrene can be seen. Figure 11B shows the double integral of the cw EPR signal from Figure 11A as a function of the activation time and shows the activation process for obtaining activated nitrenes in a dilute molecular crystal. Such plots can be used as a calibration curve for activating dopant molecules (e.g., nitrene dopant molecules) in a dilute molecular crystal. By using such a calibration curve (i.e., the amount of nitrene activated per irradiation time), nitrenes with a clearly defined density can be generated within the doped molecular crystal. A lithography method can be used to write a pattern of qubits onto a sample (e.g., a gradient, a connection region, a lattice).

[0228] Figure 12 shows exemplary cw EPR signals associated with the conversion of newly photoactivated 4-nitrenebenzoic acid in 4-iodobenzoic acid to its annealed form at room temperature.

[0229] The foregoing description has been presented for purposes of illustration. It is not exhaustive and is not limited to the precise forms or embodiments disclosed. Modifications and adaptations of the embodiments will be apparent from the specification of the disclosed embodiments and the consideration of practice. For example, although the described implementations include hardware, the systems and methods consistent with the present disclosure can be implemented using hardware and software. Further, although specific components are described as being coupled to each other, such components can be integrated with each other or distributed in any suitable manner.

[0230] Furthermore, exemplary embodiments are described herein, but the scope includes any and all embodiments having equivalent elements, modifications, omissions, combinations (e.g., of aspects across various embodiments), adaptations, or alterations based on the present disclosure. Elements of the claims should be construed broadly based on the language used in the claims and not limited to the examples described herein or the examples described during the prosecution of the application, which examples are to be construed as non-exclusive. Further, the steps of the methods of the present disclosure can be changed in any manner including rearrangement of steps, or insertion or deletion of steps.

[0231] The features and advantages of the present disclosure are apparent from the detailed description, and thus, the appended claims are intended to cover all systems and methods within the true spirit and scope of the present disclosure. As used herein, the indefinite articles “a” and “an” mean “one or more.” Similarly, the use of plural terms does not necessarily mean plural unless it is ambiguous in a given context. Further, since numerous changes and modifications can readily occur from the study of the present disclosure, it is not desired to limit the present disclosure to the exact structures and operations illustrated and described. Accordingly, all suitable changes and equivalents can be utilized so as to fall within the scope of the present disclosure.

[0232] As used herein, unless otherwise specifically stated, the term “or” includes all possible combinations except where mutually exclusive. For example, if a component is described as including A or B, then unless otherwise specifically stated or unless not practicable, the component can include A, or B, or A and B. As a second example, if a component is described as including A, B, or C, then unless otherwise specifically stated or unless not practicable, the component can include A, or B, or C, or A and B, or A and C, or B and C, or A and B and C.

[0233] Other embodiments will be apparent from the specification and practice of the embodiments disclosed herein. The specification and examples are intended to be considered only as examples, having the true scope and spirit of the disclosed embodiments as set forth by the following claims.

Claims

1. A method for generating a non-classical computer, Prepare at least one host material, The method involves embedding at least one precursor for at least one dopant molecule into the at least one host material, wherein the at least one precursor includes at least one cleavable portion. This includes cleaving the at least one cleavable portion to thereby generate the at least one dopant molecule and the at least one cleaved molecule in the at least one host material, The at least one dopant molecule includes a qubit having at least a first qubit state and a second qubit state, The aforementioned at least one dopant molecule is associated with an electronic energy level structure that includes a triplet electron manifold, The triplet electron manifold includes a first triplet state, a second triplet state, and a third triplet state. The first qubit state includes a first linear combination of the first triplet state, the second triplet state, and the third triplet state, The second qubit state includes a second linear combination of the first triplet state, the second triplet state, and the third triplet state, A method wherein the first qubit state is different from the second qubit state.

2. The method according to claim 1, wherein the at least one severable portion includes at least one optically severable portion.

3. The method according to claim 2, wherein the at least one photocleavable portion comprises at least one diazo, azide, isocyanate, or iminoiodinane portion.

4. The method according to claim 3, wherein the at least one cleaved molecule comprises at least one nitrogen molecule, a carbon monoxide molecule, or an aryl iodide molecule.

5. The method according to claim 1, wherein cutting the at least one cleavable portion includes exposing the at least one precursor to light.

6. The method according to claim 5, wherein the light has a central wavelength of about 200 nanometers (nm) to about 500 nm.

7. The method according to claim 1, wherein the at least one dopant molecule comprises a plurality of dopant molecules.

8. The method according to claim 1, wherein the host material comprises at least one organic molecule.

9. The method according to claim 1, wherein the host material includes a crystalline host material, a monocrystalline host material, a polycrystalline host material, a liquid crystalline host material, a powder host material, an amorphous host material, or a frozen solution host material.

10. The method according to claim 1, wherein the host material comprises C4-C20 linear or branched alkanes; aromatic hydrocarbons; polyaromatic hydrocarbons optionally substituted with methylene, nitrile, carbonyl, carboxylate, alkyl, deuterated alkyl, aryl, deuterated aryl, heteroaryl, deuterated heteroaryl, borane, imine, amine, nitro, phosphine, thioether, ether, fluoro, chloro, bromo, iodine, or thiocarbonyl groups; diaryl ketones; naphthalene; anthracene; pareterphenyl; benzoic acid; fluorene; biphenyl; benzene; n-hexane; biphenylene; ortho-terphenylene; meta-terphenylene; para-terphenylene; phenanthrene; di(naphthalene-2-yl)methanone; di(phenyl)methanone; or any partially or completely isotope-labeled derivative thereof.

11. The method according to claim 1, wherein the host material includes a thin film having a maximum thickness of 100 nanometers (nm).

12. The method according to claim 1, wherein the at least one dopant molecule comprises an organic molecule.

13. The method according to claim 1, wherein the at least one precursor comprises a derivative of a carbene molecule, a derivative of a nitrene molecule, a diazo derivative of a carbene molecule, an azide derivative of a nitrene molecule, an isocyanate derivative of a nitrene molecule, an imidoiodinane derivative of nitrene, (diazomethylene)dinaphthalene, (diazomethylene)dibenzene, 4-azidobenzoic acid, or any partially or completely isotope-labeled derivative thereof.

14. The method according to claim 1, wherein the at least one dopant molecule comprises a carbene molecule, a nitrene molecule, a di(naptalen-2-yl)carbene molecule, a di(phenyl)carbene molecule, or any partially or completely isotope-labeled derivative thereof.

15. The method according to claim 7, wherein the plurality of dopant molecules are arranged in a pseudo-two-dimensional (pseudo-2D) layer.

16. The method according to claim 15, wherein the pseudo-2D layer includes a self-assembled monolayer (SAM).

17. The method according to claim 1, wherein the average distance between dopant molecules is a maximum of 20 nm.

18. The at least one dopant molecule has a cubic micrometer (μm) ３ ) at least 10 ６ The method according to claim 1, wherein the dopant molecule is contained in the at least one host material at the concentration of the dopant molecule.

19. The aforementioned at least one dopant molecule comprises multiple dopant molecules, The first dopant molecule among the plurality of dopant molecules is configured to absorb a first electromagnetic energy having a first central wavelength or a first central frequency. The second dopant molecule among the plurality of dopant molecules is configured to absorb a second electromagnetic energy having a second central wavelength or a second central frequency. The method according to claim 1, wherein the first center wavelength or the first center frequency is different from the second center wavelength or the second center frequency.

20. The first center wavelength or the first center frequency is associated with a first wavelength range or a first frequency range having a first full width at half maximum (FWHM) bandwidth, The second center wavelength or the second center frequency is associated with a second wavelength range or a second frequency range having a second FWHM bandwidth, The method according to claim 19, wherein the first wavelength range or the first frequency range within the first FWHM bandwidth and the second wavelength range or the second frequency range within the second FWHM bandwidth do not overlap.

21. The method according to claim 20, wherein the first FWHM bandwidth or the second FWHM bandwidth is a maximum of 100 megahertz (MHz).

22. The method according to claim 19, wherein the first central wavelength or the second central wavelength is 200 nm to 1,000 nm.

23. The method according to claim 21, wherein the first FWHM bandwidth or the second FWHM bandwidth is at most 100 gigahertz (GHz).

24. The method according to claim 23, wherein the first center frequency or the second center frequency is 1 MHz to 100 GHz.

25. A system for performing non-classical computation, At least one host material, At least one dopant molecule contained in the at least one host material, The at least one cleaved molecule contained in the at least one host material, The at least one dopant molecule includes a qubit having at least a first qubit state and a second qubit state, The aforementioned at least one dopant molecule is associated with an electronic energy level structure that includes a triplet electron manifold, The triplet electron manifold includes a first triplet state, a second triplet state, and a third triplet state. The first qubit state includes a first linear combination of the first triplet state, the second triplet state, and the third triplet state, The second qubit state includes a second linear combination of the first triplet state, the second triplet state, and the third triplet state, A system in which the first qubit state is different from the second qubit state.

26. The system according to claim 25, wherein the at least one dopant molecule and the at least one cleaved molecule are produced by cleaving at least one precursor into the at least one dopant molecule, the at least one precursor comprising at least one cleavable portion.

27. The system according to claim 26, wherein the at least one severable portion includes at least one optically severable portion.

28. The system according to claim 27, wherein the at least one light-cuttable portion includes at least one diazo portion, azide portion, isocyanate portion, or iminoiodinane portion.

29. The system according to claim 28, wherein the cleaved molecule comprises at least one nitrogen molecule, a carbon monoxide molecule, or an aryl iodide molecule.

30. The system according to claim 26, wherein severing the at least one precursor includes exposing the at least one precursor to light.

31. The system according to claim 30, wherein the light has a central wavelength of about 200 nanometers (nm) to about 500 nm.

32. The system according to claim 25, wherein the at least one dopant molecule comprises a plurality of dopant molecules.

33. The system according to claim 25, wherein the host material comprises at least one organic molecule.

34. The system according to claim 25, wherein the host material includes a crystalline host material, a monocrystalline host material, a polycrystalline host material, a liquid crystalline host material, a powder host material, an amorphous host material, or a frozen solution host material.

35. The system according to claim 25, wherein the host material comprises C4-C20 linear or branched alkanes; aromatic hydrocarbons; polyaromatic hydrocarbons optionally substituted with methylene, nitrile, carbonyl, carboxylate, alkyl, deuterated alkyl, aryl, deuterated aryl, heteroaryl, deuterated heteroaryl, borane, imine, amine, nitro, phosphine, thioether, ether, fluoro, chloro, bromo, iodo, or thiocarbonyl groups; diaryl ketones; naphthalene; anthracene; para-terphenyl; benzoic acid; fluorene; biphenyl; benzene; n-hexane; biphenylene; or-terphenylene; meta-terphenylene; para-terphenylene; phenanthrene; di(naphthalene-2-yl)methanone; di(phenyl)methanone; or any partially or completely isotope-labeled derivative thereof.

36. The system according to claim 25, wherein the host material includes a thin film having a maximum thickness of 100 nanometers (nm).

37. The system according to claim 25, wherein the at least one dopant molecule comprises an organic molecule.

38. The system according to claim 26, wherein the at least one precursor comprises a derivative of a carbene molecule, a derivative of a nitrene molecule, a diazo derivative of a carbene molecule, an azide derivative of a nitrene molecule, an isocyanate derivative of a nitrene molecule, an imidoiodinane derivative of a nitrene molecule, (diazomethylene)dinaphthalene, (diazomethylene)dibenzene, 4-azidobenzoic acid, or any partially or completely isotope-labeled derivative thereof.

39. The system according to claim 25, wherein the at least one dopant molecule comprises a carbene molecule, a nitrene molecule, a di(naptalen-2-yl)carbene molecule, a di(phenyl)carbene molecule, or any partially or completely isotope-labeled derivative thereof.

40. The system according to claim 32, wherein the plurality of dopant molecules are arranged in a pseudo-two-dimensional (pseudo-2D) layer.

41. The system according to claim 40, wherein the pseudo-2D layer includes a self-assembled monolayer (SAM).

42. The system according to claim 25, wherein the average distance between dopant molecules is a maximum of 20 nm.

43. The at least one dopant molecule has a cubic micrometer (μm) ３ ) at least 10 ６ The system according to claim 25, wherein the dopant molecule is contained in the at least one host material at the concentration of the dopant molecule.

44. The aforementioned at least one dopant molecule comprises multiple dopant molecules, The first dopant molecule among the plurality of dopant molecules is configured to absorb a first electromagnetic energy having a first central wavelength or a first central frequency. The second dopant molecule among the plurality of dopant molecules is configured to absorb a second electromagnetic energy having a second central wavelength or a second central frequency. The system according to claim 25, wherein the first central wavelength or the first central frequency is different from the second central wavelength or the second central frequency.

45. The first center wavelength or the first center frequency is associated with a first wavelength range or a first frequency range having a first full width at half maximum (FWHM) bandwidth, The second center wavelength or the second center frequency is associated with a second wavelength range or a second frequency range having a second FWHM bandwidth, The system according to claim 44, wherein the first wavelength range or the first frequency range within the first FWHM bandwidth and the second wavelength range or the second frequency range within the second FWHM bandwidth do not overlap.

46. The system according to claim 45, wherein the first FWHM bandwidth or the second FWHM bandwidth is at most 100 megahertz (MHz).

47. The system according to claim 44, wherein the first central wavelength or the second central wavelength is 200 nm to 1,000 nm.

48. The system according to claim 45, wherein the first FWHM bandwidth or the second FWHM bandwidth is at most 100 gigahertz (GHz).

49. The system according to claim 48, wherein the first center frequency or the second center frequency is 1 MHz to 100 GHz.

50. The system according to claim 25, further comprising at least one initialization unit configured to direct a third electromagnetic energy toward the at least one dopant molecule, thereby initializing the quantum state of the at least one dopant molecule to the first qubit state or the second qubit state.

51. The system according to claim 50, wherein the third electromagnetic energy includes at least one wavelength between 200 nm and 1,000 nm.

52. The system according to claim 25, further comprising at least one non-classical action unit configured to apply a fourth electromagnetic energy to the at least one dopant molecule, thereby performing at least one non-classical action on the at least one dopant molecule.

53. The system according to claim 52, wherein the at least one nonclassical operation includes at least one quantum operation, at least one quantum computation operation, at least one quantum gate operation, at least one quantum simulation operation, or at least one quantum annealing operation.

54. The system according to claim 52, wherein the fourth electromagnetic energy includes at least one frequency between 1 MHz and 100 GHz.

55. The system according to claim 52, wherein, after performing the at least one nonclassical operation, the result of the at least one nonclassical operation correlates with the electronic state of the at least one dopant molecule.

56. The system according to claim 55, further comprising at least one storage unit configured to apply a fifth electromagnetic energy and a sixth electromagnetic energy to the at least one dopant molecule, wherein the fifth electromagnetic energy and the sixth electromagnetic energy are configured to jointly transmit information from the electronic state to the nuclear spin state of the at least one dopant molecule.

57. The system according to claim 56, wherein the fifth electromagnetic energy and the sixth electromagnetic energy are configured to jointly apply a swap gate to the at least one dopant molecule, thereby transferring the information from the electronic state of the at least one dopant molecule to the nuclear spin state.

58. The system according to claim 56, wherein the fifth electromagnetic energy includes at least one frequency between 1 kHz and 100 MHz, and the sixth electromagnetic energy includes at least one frequency between 1 MHz and 100 GHz.

59. The system according to claim 56, further comprising at least one detection unit configured to detect the electronic state of the at least one dopant molecule or the nuclear spin state of the at least one dopant molecule, thereby obtaining the result of the at least one non-classical operation.

60. The system according to claim 59, wherein the at least one detection unit is configured to apply a seventh electromagnetic energy to the at least one dopant molecule to obtain the result of the at least one non-classical operation.

61. The system according to claim 60, wherein the at least one detection unit includes at least one optical detector configured to detect light emitted by the at least one dopant molecule in response to the seventh electromagnetic energy.

62. The system according to claim 61, wherein the light emitted by the at least one dopant molecule has a first optical property associated with the first qubit state and a second optical property associated with the second qubit state, and the first optical property is different from the second optical property.

63. The system according to claim 62, wherein the first optical property or the second optical property includes the intensity, polarization, wavelength, or frequency of the light.

64. The system according to claim 25, further comprising a cryogenic unit comprising the at least one host material and configured to cool the at least one host material to a maximum temperature of 20 K.

65. The system according to claim 64, wherein the cryogenic unit includes a helium cryogenic cooler or a closed-cycle helium cryogenic cooler.

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