Quantum control operations in two-dimensional quantum computing systems

Abstract

One aspect of the disclosure relates to a method of configuring a quantum computing system, the quantum computing system including a plurality of qubits arranged on a two-dimensional (2D) lattice. The method of the disclosure includes receiving a selection of a first one or more qubits of the plurality of qubits, the first one or more qubits configured to be initialized to a predetermined information content. The method of the disclosure further includes receiving a selection of a second plurality of qubits of the plurality of qubits, the one or more qubits of the second plurality of qubits adjacent to at least one qubit each of the first one or more qubits and configured to receive the predetermined information content from at least one qubit each of the first one or more qubits. The method of the first aspect further includes receiving a selection of a third plurality of qubits of the plurality of qubits configured to perform a plurality of quantum computing operations. In the method of the first aspect, a quantum computing operation of the plurality of quantum computing operations for each qubit of the third plurality of qubits is controlled using the predetermined information content from at least one qubit each of the first one or more qubits. In the method of the first aspect, each qubit from some of the second plurality of qubits is adjacent to at least one qubit of a third plurality of qubits, and each qubit of the third plurality of qubits adjacent to a respective qubit from said some of the second plurality of qubits is configured to receive predetermined information content from said respective qubit.

Description

[Technical field]

[0001] FIELD OF THE DISCLOSURE The present disclosure relates to a method for controlling a quantum computing system, and to a remote computing system. Related aspects relate to a quantum computing system and a remote computing system. [Background technology]

[0002] There is growing interest in implementing quantum computing in various physical systems to solve a variety of real-world problems, including those dealing with chemistry, biology, solid-state physics, and cryptosystems (see, for example, E. Grumbling and M. Horowitz, “Quantum computing: Progress and Prospects” Washington, DC: The National Academies Press, 2019; https: / / doi.org / 10.17226 / 25196). The goal is to speed up computations compared to classical computers or to solve classes of problems that cannot be solved even by supercomputers that perform classical computations based on conventional algorithms. Many known quantum algorithms for use on quantum computers (e.g., quantum simulators) used to model real quantum systems require the application of a controlled unitary transformation to a subset of qubits (i.e., quantum states) that are implemented on the hardware (e.g., on a chip) of the quantum computer on which the quantum computation is performed. Here, the control of the unitary transformation is not a classical control, where a classical value controls whether or not to apply the transformation, but a quantum control, where the unitary transformation is applied depending on the state of the quantum system, thereby resulting in quantum entanglement. An example of an algorithm that requires such a controlled unitary transformation is the quantum phase estimation algorithm.

[0003] Importantly, the potential for physical realization of a quantum computer is subject to quantum decoherence associated with coupling the physical realization with the environment. However, some of the known conventional techniques for controlling quantum computation are time-consuming, such that qubits may lose coherence in time intervals shorter than those required to complete a quantum computation task. Thus, there is a need to develop new and efficient techniques for controlling quantum computing systems. Summary of the Invention

[0004] A first aspect of the disclosure relates to a method of configuring a quantum computing system, the quantum computing system including a plurality of qubits arranged on a two-dimensional (2D) lattice. The method of the disclosure includes receiving a selection of a first one or more qubits of the plurality of qubits, the first one or more qubits configured to be initialized to a predetermined information content. The method further includes receiving a selection of a second plurality of qubits of the plurality of qubits, the one or more qubits of the second plurality of qubits adjacent to at least one respective qubit of the first one or more qubits and configured to receive the predetermined information content from the respective at least one qubit of the first one or more qubits. The method of the first aspect further includes receiving a selection of a third plurality of qubits of the plurality of qubits configured to perform a plurality of quantum computing operations. In the method of the first aspect, a quantum computing operation of a plurality of quantum computing operations for each qubit of the third plurality of qubits is controlled using the predetermined information content from the respective at least one qubit of the first one or more qubits. In the method of the first aspect, each qubit from some of the second plurality of qubits is adjacent to at least one qubit of the third plurality of qubits, and each qubit of the third plurality of qubits adjacent to a respective qubit from the some of the second plurality of qubits is configured to receive the predetermined information content from the respective qubit.

[0005] A second aspect provides a quantum computing system configured according to any of the steps of the technique according to the first aspect.

[0006] A third aspect provides a quantum computing system for performing controlled quantum computational operations and adapted to perform any of the steps of the technique according to the first aspect.

[0007] A fourth general aspect of the present disclosure relates to a remote computing system comprising a quantum computing system and configured to perform a quantum computing task, the quantum computing task including a plurality of quantum computing operations performed on respective qubits according to the first aspect. The plurality of quantum computing operations of the fourth aspect can be controlled according to any of the method steps of the first aspect. The remote computing system of the fourth aspect is further configured to transmit results of the computational task to the computer-implemented system.

[0008] The techniques of the first to fourth aspects may have advantageous technical effects. First, the disclosed techniques involve performing controlled quantum computational operations on a quantum computing system comprising a hardware architecture (e.g., one or more chips) having qubits arranged in a two-dimensional lattice, which reduces the number of operations required for said control as compared to some prior art. In some cases, the number of qubit-to-qubit SWAP operations required to perform a controlled operation on a qubit increases more slowly with the number of qubits, N, as compared to some prior art. For example, in the present invention, transmitting the quantum state of an ancilla qubit used to control a computational operation on a qubit increases N with the number of qubits. 1 / 2In some cases, the present invention requires one-off operations scaled as , whereas in some prior art techniques, the transmission of the quantum state must be performed for each control operation on the qubits performed at different moments during the quantum computation. Furthermore, the number of quantum gates required to accomplish a quantum computation task can be reduced by using the qubit configuration of the present technology, thereby reducing the total decoherence or inaccuracy that occurs in the quantum computing system. That is, each quantum gate can be a potential source of decoherence and / or inaccuracy related to the fact that the physical realization of the quantum gate may not match the user-specified logical gate operation (this problem is called gate infidelity). Thus, the advantage of reducing the total number of operations on the qubits of the two-dimensional lattice required to perform a controlled computation operation on each qubit becomes more significant compared to some prior art techniques when the above two factors are considered together.

[0009] Second, the disclosed techniques enable controlled quantum computing operations to be performed in parallel, which is not possible with some conventional techniques. This can provide further speedup of controlled quantum computing operations and can result in preservation of coherence between qubits throughout the execution time of a quantum computing task.

[0010] Several terms are used herein as follows. The term "qubit" (or qubit) can refer to a quantum mechanical system with (at least) two quantum states or a superposition of these quantum states, also called two-level system for short. Two-level systems are the basic units carrying quantum information from which quantum information can be encoded and retrieved. For example, the spin of an electron in a magnetic field with two energy levels and corresponding spin-up and spin-down states is a physical realization of a qubit. Another physical realization deals with the polarization of one photon, whose two orthogonal polarizations can be considered as the two qubit states. In some cases, the two quantum states may be associated with two different energy levels, for example, with two selected energy levels in the anharmonic energy spectrum (or in other words, with two selected energy levels in an anharmonic ladder of energy levels) of the physical system that serves as the physical realization of the qubit (this may be the case, for example, of a superconducting qubit). In other cases, the two quantum states may be associated with two degenerate energy levels (i.e., they share the same energy value), which may be the case for a photonic quantum computer. The quantum state of a single qubit can be described by a wave function that can be expressed as a vector in a two-dimensional complex space, and the changes in its quantum state (for example, for the time evolution of the qubit state and / or as a result of the application of quantum gate operations) may be visualized on the Bloch sphere (see, for example, MA Nielsen and IL Chuang, “Quantum Computation and Quantum information”: 10th Anniversary Edition, Cambridge University Press, Quantum computing may involve quantum computational operations on multiple qubits such that the quantum states of the multiple qubits may be manipulated and altered (see also below). In some cases, each qubit of a multiple qubit may be treated independently of the others, in which case the quantum state of the multiple qubits may be described as a separable quantum state, i.e., represented as a tensor product of each single qubit state (and ultimately as a corresponding superposition of the quantum states of the individual qubits).In other cases, if at least two qubits from a multi-qubit system cannot be treated independently of each other (or in other words cannot be described in isolation from each other), then the multi-qubit quantum state represents an entangled state that cannot be expressed in terms of a tensor product of the individual qubit states (see also below, which describes both situations in more detail).

[0011] There are several physical realizations of systems that can be used as qubits (i.e., as two-level systems) in the context of quantum computing. The qubits of the present disclosure are not limited to a particular physical realization. An example of such a physical realization is a quantum computer based on cavity QED (cQED), where the qubits are provided by the internal states of trapped atoms coupled to a high-finesse resonator. One example of quantum computing using circuit quantum electrodynamics is superconducting quantum computing based on superconducting qubits coupled to a microwave cavity (called a quantum bus) and radiating in the microwave range, whose quantum states are manipulated by electromagnetic pulses to control the magnetic flux, charge, or phase difference across nanofabricated Josephson junctions (see, for example, https: / / doi.org / 10.1038 / nature07128). Another example relates to solid-state nuclear magnetic resonance (NMR) Kane quantum computers with qubits realized as nuclear spin states of donor atoms (e.g., phosphorus donor atoms) embedded in their respective host lattices (e.g., pure silicon lattices). In some other examples, the physical realization of a quantum computer may be based on neutral atoms in an optical lattice, where the quantum bits are realized by the internal states of neutral atoms (e.g., Rydberg atoms) trapped in the optical lattice (e.g., interacting via the Rydberg interaction) (see, e.g., https: / / doi.org / 10.1088 / 0953-4075 / 49 / 20 / 202001). In yet other examples, the quantum computer may be a quantum dot computer, where the quantum bits are given by the respective spin states of trapped electrons.

[0012] The term "quantum computational operations" and the related term "quantum computation" may refer to manipulations of quantum bits that can change their quantum state. Quantum computational operations on one or more quantum bits can be performed by quantum gates that manipulate the quantum states of the quantum bits, in other words, with the quantum information they hold. As disclosed further below, a single quantum bit can form a single-qubit quantum state (e.g., a ground state, an excited state, or a superposition of both). In some cases, multiple quantum bits can form a multi-qubit quantum state that can be in a tensor product state or an entangled state (see below for more details). Quantum gates are represented by a unitary operator U (e.g., represented by the respective unitary matrices) that ensures norm conservation of the quantum bit wave functions in the absence of dissipation, whereby the product of this operator by its Hermitian conjugate is the identity operator UU †=I, where † holds for Hermitian conjugation and I is the identity operator. Thus, quantum gates are configured to perform unitary transformations on qubits, i.e., said unitary operators representing quantum gates perform unitary transformations on the quantum states of qubits (see also the following discussion). The Hadamard gate H, the phase gate S, the π / 8 gate, and the Pauli X, Y, Z gates are examples of single-qubit gates whose actions on qubits can be visualized on the Bloch sphere as described above (see, for example, the above-mentioned book by MA Nielsen and IL Chuang). Any quantum computation on one or more qubits can be generated by a finite set of qubit gates, which are said to be universal in quantum computing. A unitary operation representing this quantum computation on a qubit can then be decomposed into a sequence of operations performed by a quantum circuit comprising gates from this finite set. Any unitary operation (e.g., a unitary operation performed on any multi-qubit logic gate) can be composed of a two-qubit Controlled-NOT (CNOT) gate and a corresponding number of single-qubit gates, i.e., single-qubit rotations, with some free parameters that characterize the unitary operation under consideration. For example, any unitary operation can be approximated (to a given accuracy) by Hadamard gates, phase gates, CNOT gates, and π / 8 gates, also called universal quantum gates (see, for example, MA Nielsen and IL Chuang, “Quantum Computation and Quantum information”: 10th Anniversary Edition, Cambridge University Press, 2010). For example, in the context of superconducting qubits, a single-qubit gate can be realized by a rotation between two energy levels of a single superconducting qubit induced by a microwave pulse transmitted on a transmission line coupled to the qubit at a frequency resonant with the energy separation between the levels.Furthermore, two-qubit gates can be realized by coupling two superconducting qubits, for example, via a microwave cavity or intermediate electrical coupling circuit (see, for example, https: / / doi.org / 10.1038 / nature02851). In the context of neutral atom quantum computing, two-qubit gates can be realized using controllable Rydberg interactions between neutral atoms that are strong enough to perform two-gate operations (see, for example, https: / / doi.org / 10.1103 / PhysRevX.10.021054).

[0013] The term "unitary transformation" as used herein as applied to a qubit should be interpreted broadly in this disclosure and may refer to a unitary transformation of the quantum state of a qubit caused by a unitary operation acting on said qubit, which may be defined by the unitary operator acting on the quantum state. For example, a quantum computing operation such as applying one or more different quantum gates (represented by respective unitary operators) to a qubit may lead to a unitary transformation of the quantum state of the qubit. In other cases, the quantum state of the qubit may evolve unitarily according to the qubit's Hamiltonian (e.g., the Jaynes-Cummings Hamiltonian of cQED), which is a Hermitian operator that determines the interaction with an external control field (e.g., a magnetic field) as well as the coupling of the qubit with a host lattice or cavity (e.g., a quantum bus in the context of superconducting quantum computing) and their possible interactions (e.g., dipole-dipole interactions in the context of Rydberg atoms). This unitary time evolution of the quantum state of a qubit (represented by a unitary time evolution operator) that occurs during quantum computing is also referred to herein as a "unitary transformation." As explained above, a single qubit rotation is a specific case of a unitary transformation.

[0014] The term "adjacency" (or the attribute "adjacent") with respect to qubits (e.g., arranged on a two-dimensional lattice) should be interpreted broadly in this disclosure, such that two qubits may be classified as adjacent if a universal quantum gate operating on the two qubits can be realized without requiring one or more individual quantum gates between either qubit of the two qubits and a third qubit, for example if a quantum computer provides all unitary operations associated with a universal set of gates operating on the two qubits without involving the third qubit, or if they are physically coupled in hardware, or if a hardware-native two-qubit gate operating on the two qubits can be realized without requiring individual quantum gates between each individual qubit of the two qubits and the third qubit, etc. In some examples, qubits may be classified as adjacent if, for example, they are nearest neighbors within the same or different types of qubits (e.g., one type may represent control qubits and another type may represent system qubits on which quantum computational operations are performed), or if the distance between the qubits under consideration is equal to or less than a certain characteristic distance (see also below). The spatial separation of qubits may be a determining factor when they directly interact with each other, for example, via dipole-dipole interactions, as is the case, for example, for dipole-dipole interactions in optically trapped Rydberg atoms (see, for example, https: / / doi.org / 10.1088 / 0953-4075 / 49 / 20 / 202001). In other examples, the spatial distance between qubits may not be a relevant factor, or at least may not be the only relevant factor determining qubit adjacency. For example, semiconductor qubits may be coupled to each other via a quantum bus to which they are coupled, such that the qubit coupling can be tuned by flux control of the qubits, and their spatial separation may not be a critical factor.For example, qubits may be considered neighbors if their qubit coupling exceeds a certain critical value, such that a two-qubit gate can be realized based on these two qubits (without a third qubit) or the two qubits can form an entangled state. In this case, their spatial separation may not be a determining factor. In some other examples, the inter-qubit coupling of superconducting qubits may be tuned by connecting them to intermediate electrical coupling circuits (see, for example, https: / / doi.org / 10.1038 / s41586-019-1666-5).

[0015] The terms "ancilla qubit" and "auxiliary ancilla qubit" refer to qubits used to control quantum computational operations and resulting unitary transformations on "system qubits." Thus, unitary transformations controlled by ancilla qubits are referred to herein as controlled unitary transformations. "Ancilla qubits" may contain predetermined information content (e.g., a known quantum state, such as an entangled state, to which they are initialized) and may transmit this information to the auxiliary ancilla qubits. Some "ancilla qubits" may be reinitialized to contain different predetermined information content, for example, during a quantum computation.

[0016] In this specification, "transmitting predetermined information content" between qubits within the same or different types of qubits should be interpreted broadly. In some cases, transmitting predetermined information content between two adjacent qubits may include applying a unitary transformation to the qubits, for example, using one or more two-qubit gates, or in some examples, one or more single- or multi-qubit gates in addition to the two-qubit gates. It should be noted that "transmitting predetermined information content" between two adjacent qubits with a unitary transformation may include direct (physical) interaction between these qubits and / or interaction of these qubits, for example, via a host lattice / quantum bus (in the above sense). In some examples herein, the "predetermined information content" may be transmitted between the distant qubits via respective unitary transformations applied between the adjacent qubits located between the distant qubits (see below for further details). In the present technology, "transmitting predetermined information content" between two adjacent qubits may include controlling a quantum computation operation performed by the qubit from which the "predetermined information content" is transmitted on the qubit to which the "predetermined information content" is transmitted, on the qubit to which the "predetermined information content" is transmitted. In some cases, the "predetermined information content" may be transmitted one or more times during (e.g., at different instants in time), for example, a quantum computation operation, in order to provide said control (see further below). Furthermore, if the "predetermined information content" can be transmitted from one qubit to another adjacent qubit in the above sense, the qubit to which the "predetermined information content" is transmitted may be said to be configured to receive the "predetermined information content".

[0017] The term "chain of qubits" as used herein should be interpreted broadly in this disclosure, referring to a one-dimensional (1D) spatial arrangement of qubits of the same type on the plane of a two-dimensional lattice (e.g., along a one-dimensional curve or line). In some cases, a type of qubit can comprise one or more connected chains of qubits extending in one or more directions. Additionally or alternatively, a type of qubit can comprise one or more unconnected chains of qubits extending in one or more directions, for example, interrupted by one or more chains of qubits of another type. [Brief description of the drawings]

[0018] [Figure 1A] 4 is a flow chart illustrating a method of controlling a quantum computing system according to a first embodiment. [Figure 1B] 4 is a flow chart illustrating further possible method steps according to the first aspect. [Figure 1C] 4 is a flow chart illustrating further possible method steps according to the first aspect. [Figure 1D] 4 is a flow chart illustrating further possible method steps according to the first aspect. [Diagram 2] 10 shows a schematic of a possible quantum computing system 1000 of the present technology with qubits arranged on a two-dimensional lattice. Unitary transformations are performed on system qubits 17 arranged in a serpentine under the control of each ancillary ancilla qubit, which forms a horizontal chain adjacent to the serpentine of system qubits. Predetermined information content (e.g., their quantum states) of ancillary qubits 15 is transmitted (i.e., overlapped) to ancillary ancilla qubits 16 as shown in this figure. Ancillary qubits 15 form a vertical chain. [Figure 3A] Figure 1 shows schematic diagrams of two possible topologies for qubit placement according to the current state of the art: (a) A two-dimensional lattice with multiple square cells with four qubits at the vertices of the square cells. Otherwise, the qubit placement is similar to that shown in Figure 2. [Figure 3B]Schematically shows two possible topologies for the arrangement of qubits according to the current technology. A two-dimensional lattice with a number of square cells rotated by 45° (around an axis perpendicular to the sheet plane) with respect to the square cells shown in FIG. 3A. The representation of the qubits by black and white circles is used to facilitate the recognition of the square cells. The ancilla qubits 15 form a straight chain (a) or a zigzag chain (b) in the vertical direction, while two straight chains (a) or zigzag chains (b) of the auxiliary ancilla qubits 16 are arranged in the horizontal direction. The system qubit represents a straight chain (a) or a zigzag chain (b) arranged both horizontally and vertically. The dashed lines in (a) and (b) indicate that it is possible to transmit a given information content between each neighboring qubit. [Figure 4] An example of a quantum circuit is shown for transmitting the predetermined information content of an ancilla qubit to each of the ancillary ancilla qubits via a series of controlled-NOT (CNOT) operations 10. A quantum computation operation (e.g., a unitary transformation) Ucontrol; 20 on the system qubits is performed under the control of the ancillary ancilla qubits, which transmit the predetermined information content to each of the system qubits (this process is shown diagrammatically by the vertical line entering the block "Ucontrol" in this figure). The quantum states of these ancillary ancilla qubits are reset after achieving the controlled unitary transformation by a series of CNOT operations. [Diagram 5] Another possible way of controlling a unitary transformation on a system qubit (not shown in this figure) using two ancilla qubits is shown. Here, a given information content of both ancilla qubits is taken into account and transmitted to the respective auxiliary ancilla qubit. As an example, this operation is performed by a Toffoli gate 30 represented by a quantum circuit comprising two Hadamard gates H; 40, one phase gate S; 60, six CNOT gates 10 and seven π / 8 gates; 50 arranged as shown in this figure. The operators † in the figure remain in the matrix representing the Hermitian conjugate of the corresponding operator T, for example the π / 8 gate. [Figure 6]1 shows diagrammatically a quantum circuit for controlling a general rotation Ra(θ);70 about axis a performed on a system qubit 17. In this embodiment, such a general rotation is performed by a quantum circuit configured to perform a rotation transformation RZ(θ / 2);90 about a rotation axis z of each qubit, a respective inverse rotation transformation RZ(−θ / 2);95, two corresponding basis rotation transformations Va,x;80, and two CNOT operations 10. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0019] First, some general aspects of the control of a quantum computing system are described before describing some possible implementations. A first aspect of the present disclosure of the control of a quantum computing system is outlined in conjunction with the flow charts shown in Figures 1A-1D. Next, exemplary topologies using qubits arranged on a quantum computing system according to the present technology are shown in Figures 2, 3A, and 3B. Next, two examples of quantum circuits for transmitting predetermined information content from an ancilla qubit to an auxiliary ancilla qubit are shown in Figures 4 and 5. Finally, an exemplary quantum circuit for controlling a general rotation on a system qubit is shown in Figure 6.

[0020] 1A-1D disclose and propose a method for configuring a quantum computing system according to a first aspect of the present disclosure. The quantum computing system of the present disclosure comprises a plurality of quantum bits arranged on a two-dimensional (2D) lattice (see, for example, Figs. 2, 3A and 3B, in which various embodiments of a 2D lattice are shown diagrammatically, and further description). Method steps of the corresponding independent claims are summarized in boxes drawn with solid lines in Figs. 1A-1D, while method steps of the dependent claims are shown in boxes drawn with dashed lines.

[0021] The present technique for configuring a quantum computing system includes receiving 100 a selection of a first one or more qubits 15; 1a-1c of a plurality of qubits, the first one or more qubits being configured to be initialized to a predetermined information content. The qubits of the first one or more qubits may be intended to control a quantum computation operation (e.g., a unitary transformation on one or more qubits) and may be referred to herein as ancilla qubits. In the example of a two-dimensional lattice shown in Figures 2, 3A, and 3B, the ancilla qubits 1a-1c are aligned along straight lines (as shown in Figures 2, 3A, with five ancilla qubits in Figure 3A) and vertical zigzag lines (as shown in Figure 3B, with five ancilla qubits therein). In some examples, the first one or more qubits may include two or more, three or more, five or more, or ten or more qubits (i.e., ancilla qubits as defined above) that include the predetermined information content. As described in more detail herein below, the predetermined information content of an ancilla qubit can include information about its quantum state, e.g., a known quantum state in which the ancilla qubit was prepared (e.g., before or during a portion of a quantum computing operation).

[0022] The next step of the technique may include receiving 200 a selection of a second plurality of qubits 16;2a-2c of the plurality of qubits, where one or more qubits 2a;2c of the second plurality of qubits are adjacent to at least one qubit 1a;1c of the first one or more qubits, respectively, and configured to receive predetermined information content from at least one qubit of the first one or more qubits (e.g., by quantum computing circuitry disclosed in connection with Figures 4 and 5, described in more detail below). In some examples, as will be made clear in more detail below, the second plurality of qubits may be required to transmit predetermined information content (e.g., their quantum state) from an ancilla qubit to a qubit (e.g., a system qubit that is not adjacent to the ancilla qubit) for which a quantum computing operation must be performed under the control of the ancilla qubit. Thus, the qubits of the second plurality of qubits may be referred to as ancillary ancilla qubits throughout this specification. In the example of the two-dimensional lattice shown in Figures 2 and 3A, the six ancillary ancillary qubits 2a-2c are members of two unlinked chains aligned along two corresponding horizontal lines, while the four ancillary ancillary qubits 2a;2b in the embodiment of Figure 3B are aligned along zigzag lines in the horizontal direction. In some examples, the second plurality of qubits (i.e., ancillary ancillary qubits according to the above definition) may include two or more, three or more, five or more, or ten or more qubits. As can be seen from Figures 3A and 3B, the ancillary ancillary qubit 2a is a nearest neighbor to the ancillary qubit 1a, which allows the ancillary ancillary qubit 2a to be further classified as a qubit that is adjacent to the ancillary qubit 1a according to the above definition. For the same reason, the ancillary ancillary qubit 2c in Figure 3A may be considered to be adjacent to the ancillary qubit 1c. Thus, in some examples, the ancillary ancilla qubits 2a and 2c described above may be configured to receive predetermined information content from ancilla qubits 1a and 1c, respectively.On the other hand, the auxiliary ancilla qubit 2b in FIG. 3A does not have a neighboring ancilla qubit because there is another auxiliary ancilla qubit 2a between the auxiliary ancilla qubit 2b and the chain of ancilla qubits. Similarly, in some cases, a neighboring ancilla qubit cannot be associated with the auxiliary ancilla qubit 2b in FIG. 3B because the distance from the auxiliary ancilla qubit 2b to the nearest ancilla qubit 1a exceeds a certain characteristic distance, which is, for example, the size of a square cell in this example. In other cases, qubit coupling can be increased (e.g., via flux control or additional electrical circuitry in the context of superconducting qubits) according to the above definition, such that in some examples two qubits may be considered to be adjacent to each other, even though they are spatially separated. Thus, in this case, qubits 1a and 2b can be classified as neighboring qubits.

[0023] The next step of the method can include receiving 300 a selection of a third plurality of qubits 17; 3a-3c out of a plurality of qubits configured to perform a plurality of quantum computing operations. In this case, one quantum computing operation (e.g., a unitary transformation for each qubit) out of the plurality of quantum computing operations for each qubit of the third plurality of qubits uses predetermined information content from at least one qubit out of the first one or more qubits (e.g., using the quantum states of one or two ancilla qubits each, as disclosed in connection with the embodiments of FIGS. 4 and 5 below) to be controllable. The qubits of the third plurality of qubits for which the quantum computing operations are controlled may be referred to as system qubits in the present disclosure. In the example of the two-dimensional lattice shown in FIGS. 2 and 3A, the 14 system qubits 3a; 3b; 3c are members of a meandering adjacent to the second plurality of qubits (i.e., auxiliary ancilla qubits), while the 13 system qubits 3a; 3b; 3c in FIG. 3B are members of a meandering adjacent to the second plurality of qubits. In some examples, the third plurality of qubits may include two or more, three or more, five or more, or ten or more qubits (i.e., system qubits according to the above definition). In some cases, the total number of qubits M of the second plurality of qubits (i.e., auxiliary ancilla qubits) can be made smaller than the total number of qubits N of the third plurality of qubits (M < N). For example, the corresponding ratio M / N may be a value of 9 / 10 or less, 1 / 2 or less, 1 / 4 or less, 1 / 10 or less.

[0024] In the techniques of the present disclosure, each qubit 2a (i.e., an auxiliary ancilla qubit) from some qubits of the second plurality of qubits is adjacent to at least one qubit 3a (i.e., a system qubit) of the third plurality of qubits. In the example of Figures 3A and 3B, possible neighboring auxiliary ancilla qubits and system qubits are designated by dashed lines. In the example of Figure 3A, each auxiliary ancilla qubit is adjacent to a respective system qubit, while in the example of Figure 3B, an auxiliary ancilla qubit is adjacent to two or three system qubits. In some examples, each qubit of the second plurality of qubits can be adjacent to at least one qubit of the third plurality of qubits (as in the embodiment shown in Figures 3A and 3B). In other examples, one or more qubits from the second plurality of qubits may not have a neighboring qubit from the third plurality of qubits. For example, one or more such ancillary ancilla qubits may be disposed between each ancillary ancilla qubit having at least one qubit of the third plurality of qubits adjacent thereto (e.g., to transmit predetermined information content therebetween). In the present technique, each qubit 3a of the third plurality of qubits (i.e., system qubits) adjacent to a respective qubit 2a (i.e., ancillary ancilla qubit) from said some of the qubits of the second plurality of qubits is configured to receive predetermined information content from said respective qubit (e.g., by the quantum computing circuit disclosed in connection with FIG. 6, see below). In other words, in this manner, predetermined information content (e.g., their quantum states) of one or more ancillary qubits may be transmitted to the system qubit via the corresponding ancillary ancilla qubit to enable control of quantum computing operations on said system qubit.

[0025] In the present technology, the first one or more qubits, the second and third qubits can be selected in the design phase of the quantum computing system. Additionally or alternatively, the first one or more qubits, the second and third qubits can be selected, for example, automatically (e.g., by a program / algorithm depending on the computational task to be performed). In other examples, the first one or more qubits, the second and third qubits can be selected by a user (e.g., via a suitable user interface). In the technology of the present disclosure, the steps 100, 200, 300 of receiving the selection of the first one or more qubits, the second and third qubits are not particularly limited, and in some cases, the qubits may be redistributed between these first one or more qubits and the two qubits (e.g., by a user or automatically as described above). For example, for one quantum computing task (see below for more details), some qubits from a plurality of qubits of a quantum computing system may be selected as members of a first one or more qubits, while for another quantum computing task, one or more qubits from the some (e.g., all of the qubits) may be selected to belong to a second and / or third plurality of qubits (e.g., to perform the quantum computing task more efficiently). In other examples, similar considerations apply to some qubits from the second and / or third plurality of qubits.

[0026] The next step of the method may include controlling the quantum computing system after performing steps 100, 200, 300 of receiving the selection (relating to the configuration of the quantum computing system). In the present technique, controlling the quantum computing system may include initializing 400 at least one qubit (i.e., an ancilla qubit) of each of the first one or more qubits to a predetermined information content (e.g., a known quantum state such as an entangled state, as described in more detail below). In a next step, the method may involve transmitting 500 the predetermined information content of at least one qubit (e.g., one qubit or two or more qubits) of each of the first one or more qubits to one or more qubits of a second plurality of qubits adjacent to the at least one qubit of each of the first one or more qubits. In other words, in accordance with the above description, the predetermined information content (e.g., their quantum states) of each of the one or more ancilla qubits may be transmitted to one or more adjacent ancilla qubits (e.g., by a quantum computing circuit disclosed in connection with Figures 4 and 5 below). Returning to the example of FIGS. 3A and 3B, the given information content of ancilla qubits 1a and 1c can be transmitted to their respective adjacent auxiliary ancilla qubits 2a and 2c.

[0027] In a next step, the predetermined information content of one or more qubits 2a;2c (i.e., auxiliary ancilla qubits) of the second plurality of qubits can be transmitted 600 to the respective other qubits 2b of the second plurality of qubits. In a preferred example, this step can be performed to transmit (in other words, distribute / propagate) the predetermined information content to a remote auxiliary ancilla qubit to which a neighboring ancilla qubit is not available (e.g., by the quantum computing circuit disclosed in connection with FIG. 4). The respective other qubits 2b of the second plurality of qubits of the present technology are configured to receive the predetermined information content from the one or more qubits 2a;2c of the second plurality of qubits. For example, as described above, there is no neighboring ancilla qubit for the auxiliary ancilla qubit 2b of FIG. 3A and FIG. 3B. In this case, the predetermined information content of the auxiliary ancilla qubit 2a received from the neighboring ancilla qubit 1a can be further transmitted (according to the above description) to the auxiliary ancilla qubit 2b.

[0028] The techniques of the present disclosure may include transmitting 700 the predetermined information content of one or more qubits 2a (i.e., auxiliary ancilla qubits) of the some of the qubits of the second plurality of qubits to one or more neighboring qubits 3a (i.e., system qubits) of the third plurality of qubits. In other words, as disclosed in further detail below and in accordance with the definitions above, the predetermined information content of the auxiliary ancilla qubit transmitted to each neighboring system qubit may be used to provide a controlled quantum computation operation on the system qubit. In some examples, the predetermined information content of one auxiliary ancilla qubit of the plurality of auxiliary ancilla qubits may be transmitted to each neighboring system qubit. For example, as disclosed further below in connection with FIG. 6, the predetermined information content of the auxiliary ancilla qubit 2a may be transmitted to each neighboring system qubit 3a shown in FIG. 3A and FIG. 3B using one or more controlled NOT (CNOT) operations 10. In some cases, the predetermined information content of each qubit of one or more qubits from the several qubits of the second plurality of qubits can be transmitted to a respective neighboring qubit of the third plurality of qubits. This situation is represented diagrammatically in the embodiment of FIG. 3A by the dashed lines drawn between the corresponding ancillary ancilla qubit and the system qubit. In some other cases, the predetermined information content of two or more, three or more, four or more qubits from the several qubits of the second plurality of qubits can be transmitted to a respective neighboring qubit of the third plurality of qubits. In other examples, the predetermined information content of one ancillary ancilla qubit of the several ancillary ancilla qubits can be transmitted to two or more neighboring system qubits, respectively. In the example of FIG. 3B, the predetermined information content of the rightmost ancillary ancilla qubit enclosed in the dashed oval can be transmitted to three different system qubits, as indicated by the respective dashed lines.In some cases, the given information content of one or more ancillary ancilla qubits (eg, each ancillary ancilla qubit) can be transmitted to two or more, three or more, four or more adjacent system qubits, respectively.

[0029] A next step of the method may include performing 800 a plurality of quantum computation operations on one or more qubits 3a-3c of the third plurality of qubits (e.g., one or more unitary transformations performed on one or more respective system qubits). The plurality of quantum computation operations on the one or more qubits may be controlled using predetermined information content transmitted to one or more qubits of the third plurality of qubits. In other words, the quantum computation operations on the system qubits may be controlled using predetermined information content transmitted to the system qubits (e.g., using their quantum states), for example, from each one or more adjacent auxiliary ancillary qubits. In some examples, the predetermined information content may be transmitted to the system qubit one or more times during the course of a quantum computation operation to provide such control (see further below and, for example, the two CNOT operations described above applied to the auxiliary ancillary qubits and system qubits shown in FIG. 6). In accordance with the disclosure above, the predetermined information content originates from each one or more ancillary qubits. In this way, quantum computation operations of the present technique performed on system qubits can be controlled by the corresponding ancilla qubits (see also Figure 2, which illustrates this control process diagrammatically). For example, quantum computation operations performed on system qubit 3a of Figures 3A and 3B can be controlled by ancilla qubit 1a via auxiliary ancilla qubit 2a, in the sense described above.

[0030] In the present technique, a qubit from a plurality of qubits on a two-dimensional lattice can be considered to be adjacent to another qubit from the plurality of qubits if the distance from the one qubit to the other qubit is equal to or less than a predetermined characteristic distance (see also definition above). In some examples, the predetermined characteristic distance can be proportional to the average distance between the qubits of the plurality of qubits arranged on the two-dimensional lattice (e.g., between the first, second and third plurality of qubits described above). In some cases, the proportionality factor between these quantities can be selected to be equal to or less than 0.5, 0.9, 1.2, 1.5, or less. In some cases, the predetermined characteristic distance can be equal to the average distance between the qubits. These two alternatives may be preferred when the two-dimensional lattice comprises square cells, such as in the embodiment shown in Figures 3A and 3B. In still other examples, some predetermined characteristic distances can be taken to identify neighboring qubits when the average distance between the qubits of the first one or more qubits is different from the average distance between the qubits of the second and / or third plurality of qubits. For example, the predetermined characteristic distance may be proportional to or equal to the respective average distances between qubits within the same or different qubits. In some cases, the value of the proportionality factor may be selected in the same way as for the single predetermined characteristic distance.

[0031] In alternative examples, the adjacencies between qubits of a plurality of qubits may be determined in different ways. In some examples, one or more qubits of a plurality of qubits arranged on a two-dimensional lattice may have at least one respective nearest neighbor qubit from one or more of the first, second, and third pluralities of qubits. In this case, at least one respective nearest neighbor qubit may be considered to be adjacent to the one or more qubits. For example, ancillary ancilla qubit 2a (a member of the second plurality of qubits) in FIG. 3A has nearest neighbor ancillary ancilla qubit 2b (another member of the second plurality of qubits), nearest neighbor ancilla qubit 1a (a member of the first one or more qubits), and nearest neighbor system qubit 3a (a member of the third plurality of qubits). In some cases, each qubit of a plurality of qubits arranged on a two-dimensional lattice may have at least one respective nearest neighbor qubit from one or more of the first, second, and third pluralities of qubits, where at least one respective nearest neighbor qubit may be considered to be adjacent to the qubit. In yet other examples, the adjacency between qubits of a plurality of qubits may be determined based on both one or more predetermined characteristic distances between the qubits defined above and the existence of respective nearest neighbor qubits.

[0032] In the disclosed techniques, the first, second and third plurality of qubits can form a corresponding number of chains on a two-dimensional lattice. In some cases, the first one or more qubits (i.e., ancillary qubits) can extend in a first direction (e.g., vertically as in FIG. 3A) with one or more chains of qubits. The second plurality of qubits (i.e., auxiliary ancillary qubits) of the disclosed techniques can extend in a second direction (e.g., horizontally as in FIG. 3A) different from the first direction. In some examples, the second plurality of qubits can comprise two or more unlinked chains of qubits (e.g., two chains of auxiliary ancillary qubits are shown in FIG. 3A). In some cases, the third plurality of qubits (i.e., system qubits) can comprise multiple linked chains of qubits, where each chain of the multiple linked chains of the third plurality of qubits extends in either the first direction or the second direction (e.g., horizontally and vertically as shown in FIG. 3A and FIG. 3B). In some examples, one or more chains (e.g., each chain) from the multiple linked chains of the third plurality of qubits extending in the second direction can be connected to a corresponding chain from the multiple linked chains of qubits extending in the first direction. It should be noted that the first, second and third pluralities of qubits extending in the first and / or second directions should be interpreted broadly in this disclosure. In some examples, the shape of the corresponding chains of qubits can form a one-dimensional (1D) curve on the plane of a two-dimensional lattice extending in the respective direction.

[0033] In one topology of the present technology using qubits arranged on a two-dimensional lattice, the first one or more qubits can form a chain linearly aligned in a first direction (e.g., a vertical chain of ancillary qubits in FIG. 3A). Additionally, each chain of two or more unlinked chains of the second plurality of qubits can be linearly aligned, respectively, in the second direction (e.g., two horizontal unlinked chains of ancillary ancillary qubits in FIG. 3A). In some cases, each chain of the multiple linked chains of the third plurality of qubits can be linearly aligned, respectively, in either the first or second direction (e.g., two vertical chains of system qubits are connected corresponding to three horizontal chains of system qubits in FIG. 3A). In some examples, the multiple linked chains can be arranged in a serpentine shape adjacent to the second plurality of qubits extending in the first direction (e.g., the serpentine of system qubits extends vertically as shown in FIG. 3A). In some cases, multiple chains from the multiple connected chains aligned in the second direction are interrupted in each second chain by corresponding chains from two or more unconnected chains of the second multiple of qubits (e.g., see FIG. 3A where two horizontal chains from a meander of system qubits are interrupted by two horizontal unconnected chains of auxiliary ancilla qubits).

[0034] In an alternative topology of the present technology, the first one or more qubits form chains aligned in a zigzag line in a first direction (e.g., zigzag chains of ancillary qubits as shown in FIG. 3B). Additionally, each chain of two or more unlinked chains of the second plurality of qubits can be aligned in a respective zigzag line in a second direction (e.g., see the zigzag horizontal chains of ancillary ancillary qubits shown in FIG. 3B). In some cases, each chain of the multiple linked chains of the third plurality of qubits can be aligned in a respective zigzag line in either the first or second direction (e.g., in FIG. 3B, one vertical zigzag chain of system qubits is correspondingly connected to two horizontal zigzag chains of system qubits). In some examples, similar to the embodiment of FIG. 3A, the multiple linked chains can be arranged in a serpentine shape adjacent to the second plurality of qubits extending in the first direction (e.g., the serpentine of system qubits extends vertically as shown in FIG. 3B). In some cases, multiple chains from the multiple connected chains aligned in the second direction are interrupted in each second chain by corresponding chains from two or more unconnected chains of the second multiple of qubits (e.g., two zigzag horizontal chains from a meander of system qubits are interrupted by a zigzag horizontal chain of auxiliary ancilla qubits, see FIG. 3B).

[0035] In some examples of the present disclosure, each chain of two or more unlinked chains of the second plurality of qubits (i.e., auxiliary ancilla qubits) can include a single qubit adjacent to a respective qubit of the first one or more qubits (i.e., ancilla qubits), where the single qubit is separated from the respective qubit by a first predetermined distance. Returning to the example of Figures 3A and 3B, two auxiliary ancilla qubits 2a and 2c are adjacent to ancilla qubits 1a and 1c, respectively, and separated from the ancilla qubits 1a and 1c by a distance equal to the distance between the two nearest auxiliary ancilla qubits (e.g., the distance between the two nearest auxiliary ancilla qubits can be the same for all auxiliary ancilla qubits). In some examples, the first predetermined distance can be proportional to the distance between the two nearest auxiliary ancilla qubits (e.g., the proportionality factor between these quantities is 2.0 or less, 1.0 or less, or 0.5 or less). Additionally, each chain of the two or more unlinked chains of the second plurality of qubits can be separated from each subsequent chain of the two or more unlinked chains of qubits by a second predetermined distance (e.g., the second predetermined distance corresponds to the distance between the two horizontal chains of auxiliary ancilla qubits enclosed by the two dashed ellipses shown in FIG. 3A). In some examples, a set of subsequent chains from the multiple linked chains of the third plurality of qubits aligned in the second direction can be separated by a third predetermined distance if the set of chains is uninterrupted (e.g., see two consecutive horizontal chains of system qubits in FIG. 3A), and otherwise, the set of subsequent chains can be separated by a fourth predetermined distance (e.g., see two interrupted horizontal chains of system qubits in FIG. 3A). In some examples, the first and third predetermined distances can be equal. Additionally or alternatively, the second predetermined distance can be three times longer than the first predetermined distance. Further, in addition or alternatively, the fourth predetermined distance may be twice as long as the first predetermined distance.

[0036] In one example of the present technology, the two-dimensional lattice can be a rectangular lattice. In another example, the two-dimensional lattice can be a square lattice. In yet another example, the two-dimensional lattice can be any other two-dimensional shape (e.g., a polygon, a rectangle, a pentagon, a hexagon, a parallelogram, a circle, or a triangle). In some examples, multiple qubits from a plurality of qubits arranged in a two-dimensional lattice can be equally spaced. For example, all qubits from one or more of a first, second, and third plurality of qubits can be equally spaced. In some cases, all qubits in a two-dimensional lattice can be equally spaced. Furthermore, in some cases, a two-dimensional lattice (e.g., a rectangular or square lattice) can comprise a plurality of square cells having four qubits at the vertices of the square cells, where each qubit from the four qubits is a qubit from one of the first, second, and third plurality of qubits. In the qubit topology of FIG. 3A, there are square cells having different combinations of ancilla qubits, ancillary ancilla qubits, and system qubits. For example, one square cell may comprise only a system qubit, while another may comprise all listed types of qubits. A similar situation can be seen in the other qubit topology shown in FIG. 3B, where the two-dimensional lattice comprises a plurality of square cells rotated 45° (around an axis perpendicular to the sheet plane) relative to the square cells shown in FIG. 3A. Additionally or alternatively, the two-dimensional lattice can comprise a plurality of square cells (e.g., rectangular cells) having four qubits at the vertices of the square cells (e.g., rectangular cells), where each qubit from the four qubits is a qubit from one of a first, second, and third plurality of qubits. Additionally or alternatively, the two-dimensional lattice can comprise a plurality of triangular cells having three qubits at the vertices of the triangular cells, where each qubit from the three qubits is a qubit from one of a first, second, and third plurality of qubits.

[0037] In the techniques disclosed herein, the predetermined information content of a first one or more qubits (i.e., ancilla qubits) is determined by the quantum state of the one or more qubits.

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[0038] The techniques of the present disclosure may further include initializing 410 at least one qubit of each of the first one or more qubits (i.e., ancilla qubits) to a quantum state (e.g., a multi-qubit or single-qubit quantum state as disclosed above). For example, such initialization may be performed by respective quantum circuits comprising single and / or multi-qubit qubit gates (e.g., two- and / or three-qubit gates) to prepare the one or more ancilla qubits in the respective quantum state. In a next step, the method may include transmitting 510 information regarding the quantum state of one qubit of each of the at least one qubit of the first one or more qubits from said one qubit to a single qubit of a corresponding chain of two or more unconnected chains of a second plurality of qubits, said single qubit being adjacent to one qubit of each of the at least one qubit of the first one or more qubits. For example, information regarding the quantum state of ancilla qubit 1a may possibly include information regarding other ancilla qubits from a chain of ancilla qubits (e.g., in the case of entangled states introduced above), and that information may be transmitted to adjacent ancilla qubit 2a (see FIGS. 3A and 3B). Information regarding the quantum state of ancilla qubit 1c from FIG. 3A may, for example, be transmitted to adjacent ancilla qubit 2c in a similar manner. Thus, in some examples, information regarding the quantum state of one qubit of each of at least one qubit of the first one or more qubits may be transmitted from said one qubit of a respective qubit to a single qubit of several corresponding chains (e.g., each corresponding chain) of two or more unconnected chains of a second plurality of qubits, said single qubit being adjacent to one qubit of each of at least one qubit of the first one or more qubits.

[0039] A next step of the technique may include transmitting 610 information about the quantum state from a single qubit in a corresponding chain of two or more unconnected chains of the second plurality of qubits to a respective adjacent qubit in the chain. For example, the auxiliary ancilla qubit 2a in Figures 3A and 3B may transmit the information about the quantum state received from the adjacent ancilla qubit 1a consistent with the above description to the adjacent ancilla qubit 2b relative to the auxiliary ancilla qubit 2a. The method of the first aspect may further include iteratively transmitting 620 information from each adjacent qubit in the chain to a next qubit in the chain adjacent to the respective adjacent qubit (e.g., the auxiliary ancilla qubit 2b in Figure 3A may transmit information to an adjacent qubit to the right of it). In this case, the next qubit in the chain may be considered to be the respective adjacent qubit for the next iteration. In some examples, repeatedly transmitting 620 information in a corresponding one of two or more unconnected chains of the second plurality of qubits may be performed until information has been transmitted to several qubits (e.g., each qubit) in the corresponding one of the two or more unconnected chains. In other words, information regarding the quantum state of an ancilla qubit (e.g., ancilla qubit 1a in FIGS. 3A and 3B) may be transmitted first to a respective adjacent ancilla qubit (e.g., ancilla qubit 2a in FIGS. 3A and 3B) and then to other (distant) ancilla qubits in the chain (e.g., first to ancilla qubit 2b and then to the other ancilla qubit located to the right of this qubit 2b in the same chain).

[0040] In one embodiment, the technique may include initializing one or more qubits in a corresponding chain of two or more unconnected chains of the second plurality of qubits to a zero quantum state |0〉. Thus, in this example, the ancillary qubits of the corresponding chain are initialized to the ground state introduced above. In a next step, the aforementioned sending steps 510, 610, 620 may be performed using several successive controlled NOT (CNOT) operations 10 between adjacent qubits of each of the two or more unconnected chains, as shown in FIG. 4. Specifically, the function of each CNOT operation of the quantum circuit of FIG. 4 (block U indicating a subsequent controlled quantum computation operation, e.g., a controlled unitary transformation, to be performed on the system qubits described below) is determined if the previous qubit has a quantum state |1〉 (immediately preceding the respective symbol denoted by ·) or, otherwise, if the previous qubit has a quantum state |0〉 and the quantum state of the subsequent qubit is left unchanged. control The four CNOT gates before 10) are

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[0041] In some examples of the present technology, one or more CNOT operations from the several consecutive CNOT operations introduced above can be performed by respective quantum CNOT gates. Additionally or alternatively, one or more CNOT operations may include decomposing the one or more CNOT operations into corresponding quantum operations that are performed by native hardware gates (i.e., gates available in a particular architecture of a quantum computer and / or qubit topology), respectively.

[0042] The techniques of the present disclosure may further include resetting 630 one or more qubits (i.e., ancillary qubits) of each of the second plurality of qubits to a zeroth quantum state |0〉 after performing one or more quantum computation operations (e.g., one or more unitary transformations performed on the system qubits) of the plurality of quantum computation operations on one or more qubits 3a-3c of the third plurality of qubits to which each one or more qubits of the second plurality of qubits transmitted the predetermined information content. In some cases, resetting the ancillary ancillary qubits to the zeroth quantum state after achieving a first portion of a quantum computation operation on the system qubits may be necessary to enable the respective ancillary qubits to control a subsequent portion of the quantum computation operation on those system qubits. For example, the predetermined information content of each ancillary qubit may be changed (e.g., initialized to another quantum state) after the first portion of the quantum computation operation is performed. In this case, the auxiliary ancilla qubits may be reset to the zeroth state prior to receiving information regarding the quantum state of each ancilla qubit to avoid possible interference / mixing with the previous quantum state of the auxiliary ancilla qubit. In some examples, the resetting step 630 may include applying several successive CNOT operations 10 between adjacent qubits of each of the two or more disjoint chains. In one non-exhaustive embodiment, the several successive CNOT operations 10 previously used in the sending steps 510, 610, and 620 may be applied to the auxiliary ancilla qubits in the reverse order (block U). control (see the four CNOT gates 10 in Figure 4 which are applied to the auxiliary ancilla qubits 4−1 after

[0043] Additionally or alternatively, the method may include initializing 415 at least two qubits of each of the first one or more qubits to a quantum state similar to the previous embodiment. For example, such initialization may be performed by respective quantum circuits comprising single and / or multi-qubit gates (e.g., two and / or three-qubit gates) to prepare one or more ancilla qubits to a respective quantum state. In a next step, the method may include transmitting 515 information regarding the quantum state of the at least two qubits of each of the first one or more qubits (e.g., the quantum state of the multi-qubit of at least two ancilla qubits) from said qubits to a single qubit of a corresponding chain of two or more unconnected chains of a second plurality of qubits (i.e., to a single ancilla qubit), where said single qubit is adjacent to one or more qubits of each of the at least two qubits of the first one or more qubits. In some cases, a single qubit (i.e., a single ancillary qubit) of a corresponding chain may be adjacent to at least two qubits (e.g., all qubits of at least two qubits each) of the first one or more qubits. For example, information about the quantum states of two ancillary qubits 1a and 1b of FIG. 3B (e.g., entangled states involving only these two qubits or these qubits together with some other ancillary qubits of this chain) may be transmitted to an adjacent ancillary ancillary qubit 2a. Thus, in some examples, information about the quantum states of at least two qubits each from said qubit may be transmitted to a single qubit of some corresponding chains (e.g., each corresponding chain) of two or more unconnected chains of the second plurality of qubits. In the example of FIG. 3B, said single qubit (i.e., ancillary ancillary qubit 2a) is adjacent to at least two qubits (i.e., two ancillary qubits 1a and 1b of FIG. 3B) of the first one or more qubits.In yet other examples, a single qubit in a corresponding chain may be adjacent to more than two qubits, but less than the total number of qubits of at least two qubits each of the first one or more qubits.

[0044] In the present technique, transmitting 515 information regarding the quantum state of each of the at least two qubits of the first one or more qubits may include transmitting information regarding the quantum state of each of the at least two qubits of the first one or more qubits that are not adjacent to the single qubit to a qubit of each of the at least two qubits of the first one or more qubits that is adjacent to the single qubit in a corresponding chain of two or more unconnected chains of a second plurality of qubits. For example, if a qubit adjacent to a single qubit and a qubit that is not adjacent to the single qubit are adjacent to each other, the non-adjacent qubit and adjacent qubit may exchange information regarding their quantum states via a single SWAP operation (i.e., an operation that exchanges information of these two qubits, or decomposing this operation into native hardware gates, see below for further details). In other cases, when the non-adjacent qubit and the neighboring qubit are not adjacent to each other with respect to the single qubit, exchanging information between them may include repeatedly applying several subsequent SWAP operations between the neighboring qubits of at least two qubits of the first one or more qubits disposed between the non-adjacent qubit and the neighboring qubit. In particular, the application of several subsequent SWAP operations may be performed repeatedly until information regarding the quantum state of the non-adjacent qubit (i.e., the ancilla qubit that is not adjacent to the respective ancillary ancilla qubit) is transmitted to the neighboring qubit (i.e., the ancilla qubit that is adjacent to the respective ancillary ancilla qubit). The information of the non-adjacent qubit regarding its quantum state transmitted to the neighboring qubit (e.g., by the SWAP operation disclosed above) may be further transmitted from the neighboring qubit to the single qubit of a corresponding chain of two or more unconnected chains of the second plurality of qubits in a manner similar to that further described above in connection with FIG. 4.In a preferred embodiment, information on the quantum state of a qubit from at least two qubits each of the first one or more qubits adjacent to the single qubit can first be transmitted from these qubits to the single qubit. In a next step, a SWAP operation can be applied to the qubits that are not adjacent to the single qubit, as described above, in order to further transmit information on its quantum state to the single qubit. In some cases, after performing the step of transmitting information on the quantum state of the non-adjacent qubits, several subsequent SWAP operations can be performed in reverse order until the quantum states of the participating qubits are returned from the first one or more qubits to their previous (e.g., initial) quantum state before the SWAP operation was applied. In some cases, the procedure described above can be applied to several qubits (e.g., each qubit) from at least two qubits of the first one or more qubits that are not adjacent to the single qubit.

[0045] For example, the method steps disclosed in the previous paragraph may be clarified by the embodiment shown in FIG. 3A. Specifically, the adjacent ancillary ancilla qubit 2a in FIG. 3A is adjacent to the ancilla qubit 1a, while the adjacent ancillary ancilla qubit 2a is not adjacent to the ancilla qubit 1b (e.g., because the latter is not a nearest neighbor in the sense further described above). In this case, information regarding the quantum state of the ancilla qubit 1b and the quantum state of the ancilla qubit 1a can be exchanged between these qubits via a single SWAP operation (or decomposition into native hardware gates), whereby the information regarding the quantum state of the ancilla qubit 1b is (physically) located in the ancilla qubit 1a. This information (i.e., information regarding the quantum state of the ancilla qubit 1b) can then be further transmitted from the ancilla qubit 1a to the adjacent ancilla qubit 2a, as further disclosed above in relation to, for example, FIG. 4. Finally, an inverse SWAP operation can be applied to ancilla qubits 1b and 1a to restore their previous (eg, initial) quantum states before the SWAP operation was applied. The next step of the technique may include transmitting 615 information about a quantum state from a single qubit in a corresponding chain to a respective neighboring qubit in the chain of a second plurality of qubits. For example, the auxiliary ancilla qubit 2a in FIG. 3A or FIG. 3B may transmit the information about the quantum state (received from two ancilla qubits 1a and 1b, where only ancilla qubit 1a is neighboring auxiliary ancilla qubit 2a as in FIG. 3A, or where both ancilla qubits 1a and 1b are neighboring auxiliary ancilla qubit 2a as in FIG. 3B) to the auxiliary ancilla qubit 2b that is neighboring to the auxiliary ancilla qubit 2a. The method may further include repeatedly transmitting 625 information from each neighboring qubit in the chain to the next qubit in the chain that is neighboring to the respective neighboring qubit (e.g., the auxiliary ancilla qubit 2b in FIG. 3A or FIG. 3B may transmit information to a neighboring qubit to the right of it, as in the previous embodiment). In this case, the next qubit in the chain can be considered to be the respective neighboring qubit for the next iteration. In some examples, repeatedly transmitting information in a corresponding one of two or more unconnected chains of the second plurality of qubits 625 can be performed until information is transmitted to some qubits (e.g., each qubit) in the corresponding one of the two or more unconnected chains. In other words, information about the quantum state of an ancilla qubit (e.g., two ancilla qubits 1a and 1b in FIG. 3A or FIG. 3B) can be transmitted first to a respective neighboring ancilla qubit (e.g., to ancilla qubit 2a in FIG. 3A and FIG. 3B) and then to other (distant) ancilla qubits in the chain (e.g., first to ancilla qubit 2b and then to other ancilla qubits located to the right of this qubit 2b in the same chain). In one embodiment, the technique may include initializing one or more qubits in a corresponding chain of two or more unconnected chains of the second plurality of qubits to a zero quantum state |0〉 (similar to the description in connection with the embodiment shown in FIG. 4). Thus, in this example, the ancillary ancillary qubits of the corresponding chain are initialized to their basis states introduced above. In a next step, a three-qubit quantum gate acting on two qubits (i.e., each ancillary qubit) of the first one or more qubits and a single qubit (i.e., a single ancillary ancillary qubit) of the corresponding chain of two or more unconnected chains of the second plurality of qubits may be used to transmit information about the quantum states of each of the two or more qubits to the single qubit. For example, in the embodiment of FIG. 5, information about the quantum states of the two ancillary qubits 1 and 2 is transmitted to the ancillary ancillary qubit 1 using a three-qubit quantum gate. In some cases, as in the embodiment shown in FIG. 5, the three-qubit quantum gate may be a Toffoli gate 30. In one non-exhaustive example, a Toffoli gate can be a quantum circuit comprising several Hadamard gates H;40, several phase gates S;60, several CNOT gates, and several π / 8 gates T;50 arranged in a corresponding order, for example as shown in FIG. 5 (see, for example, MA Nielsen and IL Chuang, “Quantum Computation and Quantum information”: 10th Anniversary Edition, Cambridge University Press, 2010). Hadamard gates, phase gates, and π / 8 gates are single qubit gates known to those skilled in the art. In some examples, the operations performed by one or more of the Hadamard gates, π / 8-gates, phase gates, and CNOT gates may include decomposing the operations into corresponding quantum operations performed by native hardware gates, respectively.In some examples, when two qubits of the first one or more qubits are both adjacent to a single qubit, information about the quantum state of each of the two or more qubits can be sent directly to the single qubit (e.g., without the SWAP operation described above). In other examples, when one of the two qubits of the first one or more qubits is not adjacent to a single qubit (e.g., ancilla qubit 1 of FIG. 5 is not adjacent to auxiliary ancilla qubit 1), information about the quantum state of the non-adjacent qubit can be sent from the non-adjacent qubit to another qubit from the two qubits of the first one or more qubits that are adjacent to the single qubit (e.g., from ancilla qubit 1 of FIG. 5 to ancilla qubit 2 adjacent to auxiliary ancilla qubit 1). For example, the SWAP operation between ancilla qubits 1 and 2 of FIG. 5 can be applied immediately before each of the CNOT operations between ancilla qubit 1 and auxiliary ancilla qubit 1 of FIG. 5. Next, a CNOT operation may be applied between ancilla qubit 2, which contains information about the quantum state of ancilla qubit 1, and ancillary ancilla qubit 1. This would be equivalent to a CNOT operation being performed between ancilla qubit 1 and ancillary ancilla qubit 1. In a next step, an inverse SWAP operation may be applied to two qubits (i.e., ancilla qubits 1 and 2) of the first one or more qubits to restore their previous (e.g., initial) quantum states before the SWAP operation was applied.

[0046] In a next step, similar to the previous embodiment shown in FIG. 4, several successive CNOT operations can be used to perform the steps related to transmitting 615 information about the quantum state from a single qubit of a corresponding chain to a respective neighboring qubit of said chain of a second plurality of qubits (e.g., from auxiliary ancilla qubit 1 in FIG. 5 to auxiliary ancilla qubit 2 in FIG. 4), and repeatedly transmitting 625 said information from each neighboring qubit of said chain to the next qubit of the neighboring chain for each neighboring qubit (e.g., from auxiliary ancilla qubit 2 to other auxiliary ancilla qubits 3 and 4 as shown in FIG. 4). Similarly, one or more CNOT operations from said several successive CNOT operations introduced above can be performed by respective quantum CNOT gates 10, as disclosed in connection with the embodiment of FIG. 4. Additionally or alternatively, one or more CNOT operations may include decomposing said one or more CNOT operations into corresponding quantum operations performed by native hardware gates, respectively. In some examples, step 630 of resetting one or more qubits (i.e., auxiliary ancilla qubits) of each of the second plurality of qubits may be performed in a manner similar to that described further above in connection with the embodiment shown in FIG.

[0047] The techniques of the present disclosure may further include transmitting the predetermined information content (e.g., the quantum state of an ancilla qubit) to a qubit of a third plurality of qubits for which a neighboring qubit from the second plurality of qubits is unavailable (i.e., no neighboring auxiliary ancilla qubit is available) (e.g., to a system qubit of a corresponding chain on which one or more of the quantum computation operations must be performed). In the techniques of the present disclosure, this transmitting step may include transmitting the predetermined information content from a qubit of one or more qubits of the some of the qubits of the second plurality of qubits (i.e., an auxiliary ancilla qubit) to a qubit of one or more neighboring qubits of each of the third plurality of qubits (i.e., a system qubit adjacent to the auxiliary ancilla qubit) by applying a SWAP operation (i.e., an operation that swaps the quantum states of the two qubits under consideration) to the qubit. For example, system qubit 3c shown in the embodiment of Figures 3A and 3B is a system qubit that does not have a neighboring auxiliary ancilla qubit. In this case, the predetermined information content from each adjacent ancillary qubit can be transmitted to the system qubit 3b by a SWAP operation consistent with the disclosure above (the dashed lines in both figures indicate the adjacency between the system qubit 3b and its partner among the multiple ancillary qubits).

[0048] The next step of the method may include transmitting the predetermined information content from a qubit of one or more respective adjacent qubits of the third plurality of qubits to a qubit of the third plurality of qubits for which a neighboring qubit from the second plurality of qubits is unavailable by repeatedly applying several subsequent SWAP operations between adjacent qubits of the third plurality of qubits located between said qubits. In some cases, the repeated application of several subsequent SWAP operations is performed until the predetermined information is swapped to a qubit of the third plurality of qubits adjacent to a qubit of the third plurality of qubits for which a neighboring qubit from the second plurality of qubits is unavailable. In other words, SWAP operations between adjacent system qubits are performed until the predetermined information of said auxiliary ancilla qubit is swapped to a system qubit adjacent to a system qubit that does not have a neighboring auxiliary ancilla qubit.

[0049] Returning to the example of Figures 3A and 3B, the above system qubits 3c and 3b are adjacent, so that in this case no SWAP operation is required (system qubit 3b contains the predetermined information of the auxiliary ancilla qubit according to the above description). On the other hand, one SWAP operation may be required between system qubits 3c and 3b to transmit the predetermined information content to the system qubit located in the lower right corner of the two-dimensional lattice of Figure 3A. In some cases, the number of SWAP operations required may be proportional to (e.g., equal to) the number of system qubits between the respective auxiliary ancilla qubit (from which the predetermined information content is transmitted) and the system qubit for which the adjacent auxiliary ancilla qubit is unavailable. It should be noted that the use of auxiliary ancilla qubits in the present techniques may reduce some of the time-consuming SWAP operations required to provide control because some system qubits may have adjacent auxiliary ancilla qubits (e.g., 50% or more, 75% or more, 90% or more, 95% of the total number of system qubits N may have adjacent auxiliary ancilla qubits). Thus, in some examples of the present techniques, the number of SWAP operations required for control may be independent of N, whereas in some prior art techniques, the number of SWAP operations may be independent of N. 1 / 2 may be proportional to

[0050] The techniques of the present disclosure may further include transmitting predetermined information content from a qubit of the third plurality of qubits adjacent to a qubit of the third plurality of qubits for which a neighboring qubit from the second plurality of qubits is unavailable to the qubit of the third plurality of qubits for which a neighboring qubit from the second plurality of qubits is unavailable (e.g., transmitting the predetermined information content from system qubit 3c of FIG. 3A to a system qubit located in the lower right corner of the two-dimensional lattice of FIG. 3A). In the present techniques, a qubit of the third plurality of qubits for which a neighboring qubit from the second plurality of qubits is unavailable may be configured to receive the predetermined information content from the neighboring qubit of the third plurality of qubits. Thus, the predetermined information content (e.g., its quantum state) of each ancillary qubit is physically contained in a system qubit adjacent to a system qubit that does not have a neighboring ancillary ancillary qubit and may be transmitted from the neighboring system qubit to a system qubit that does not have a neighboring ancillary ancillary qubit. In some examples, as described further below in connection with FIG. 6, transmitting the predetermined information between these system quantum bits may be performed in a manner similar to that used to transmit the predetermined information between the auxiliary ancillary quantum bit and each adjacent system quantum bit, e.g., using a number of CNOT operations (e.g., two CNOT operations) between these quantum bits to provide the control.

[0051] In a next step, the method herein may include performing a plurality of quantum computation operations on qubits of the third plurality of qubits for which no neighboring qubits from the second plurality of qubits are available under control of the transmitted predetermined information (e.g., in a manner similar to that shown in the embodiment of FIG. 6, see the following description). In some cases of the present technology, after performing one or more operations from the plurality of quantum computation operations on said qubits (under control of the transmitted predetermined information), the method may further include performing several subsequent SWAP operations in reverse order until the quantum states of qubits from the third plurality of qubits participating in the SWAP operation are restored to their previous quantum states before the SWAP operation was applied. In some cases, the above procedure may be applied to some qubits (e.g., each qubit) of the third plurality of qubits for which no neighboring qubits from the second plurality of qubits are available.

[0052] In some examples of the present technology, the several SWAP operations can be performed by respective quantum circuits to exchange two quantum bits. In some examples, each quantum circuit can include three CNOT quantum gates known to those skilled in the art (see, for example, MA Nielsen and IL Chuang, “Quantum Computation and Quantum information”: 10th Anniversary Edition, Cambridge University Press, 2010). Additionally or alternatively, one or more SWAP operations can include decomposing the SWAP operation into corresponding quantum operations each performed by a native hardware gate. In the techniques of the present disclosure, performing 800 the plurality of quantum computation operations includes performing one or more control unitary transformations 810 applied to each qubit (i.e., system qubit) of the third plurality of qubits, thereby changing the quantum state of the respective qubit, and the one or more unitary transformations applied to each qubit may be controlled using predetermined information content transmitted to the respective qubit in accordance with the above description. For example, the predetermined information content (e.g., the quantum state of each of the one or more ancilla qubits) may be transmitted to each qubit one or more times (i.e., at different instants in time) during the course of the quantum computation operation using several CNOT operations (e.g., two CNOT operations) to provide the control (see FIG. 6 and the description below). In some examples, the one or more unitary transformations for each qubit may be performed by one or more corresponding quantum single qubit gates acting on the respective qubit (e.g., different quantum single gates may act on the respective qubit at different instants or time intervals). In some cases, one or more unitary transformations performed by one or more quantum single qubit gates can result in a unitary time evolution of the quantum state of the respective qubit. In some examples, multiple unitary transformations can be performed on some qubits (e.g., all qubits) of a third plurality of qubits (i.e., system qubits) under control of respective qubits from the first one or more qubits. In some cases, the multiple unitary transformations can form a quantum computing task that is performed in parallel and / or sequentially on the some qubits of the third plurality of qubits (i.e., system qubits).

[0053] In the present technique, performing one or more controlled unitary transformations on each qubit of the third plurality of qubits (i.e., system qubits) includes performing a controlled rotation transformation R applied to each qubit. a(θ); 70 (see FIG. 6 and the following description), where the rotation transformation is defined by a predetermined rotation angle θ about a predetermined axis a. The angle θ can be determined when a quantum computing task including a controlled rotation is compiled, for example when performing a quantum computing task related to a controlled simulation of a time evolution defined by a quantum Hamiltonian of a quantum system of interest (e.g., dealing with quantum chemistry or condensed matter physics). In this setting, the angle θ can be pre-determined by the amplitude of a particular term of the Hamiltonian and the time to be simulated, for example when using quantum phase estimation (QPE) to determine the ground and / or excited states of a Hamiltonian system. In another example, the angle θ can be pre-determined after the quantum computing task is compiled, but before the quantum computing task is executed. This is the case, for example, for variational or hybrid quantum-classical algorithms, where the quantum computing task is combined with a classical minimization and the value of θ is determined by the classical part of the hybrid algorithm as part of the minimization of a cost function. A series of such controlled rotation transformations may be used, for example, in quantum phase estimation algorithms or variational hybrid quantum-classical algorithms. In some cases, the rotation transformation R a (θ); 70 is the basis rotation transformation V a,z The method may include applying 830 a basis rotation transformation V(x,y) to each qubit (i.e., a rotation of the basis vectors on which the quantum state of each qubit is defined), where the basis rotation transformation corresponds to a rotation of a given axis a about a rotation axis z of the respective qubit. For example, the quantum state of each qubit may be defined as a vector on the Bloch sphere, and the basis rotation transformation may correspond to a rotation of the Bloch basis vectors. In one example, the basis rotation transformation V(x,y) shown generally in FIG. a,z can be defined by the corresponding operators represented, for example by the respective rotation matrices. Similarly, a controlled rotation transformation R a(θ) is defined by an operator that can be expressed by a corresponding rotation matrix acting on the quantum state of each qubit represented on the Bloch sphere.

[0054] In a next step, the method calculates a rotation transformation R about a rotation axis z. z (θ / n) to the respective qubit, where the rotation transformation may be defined as a fraction of a predetermined rotation angle about a rotation axis z, θ / n;90, where n represents an integer. In some examples, the rotation transformation R z (θ / 2) is defined by an operator that can be expressed as a 2×2 matrix, for example, by the following equation:

number

[0055] In the embodiment of FIG. 6, n=2, so in this example, the rotation transformation R z (θ / 2) may be defined by half θ / 2;90 of a predetermined rotation angle about a rotation axis z. The method of the first aspect may then include applying 850 a CNOT operation 10 to each qubit and a qubit from one or more qubit neighbors of said respective qubit that is used to control one or more unitary transformations for said respective qubit. Thus, by applying the CNOT operation, a predetermined information content is transferred from said neighboring qubits to a controlled rotation transformation R a(θ);70 may be transmitted to each qubit to which it is applied. In accordance with the above discussion, if a neighboring ancillary qubit is not available for a respective qubit, then the qubit (or control qubit, for short) used to control one or more unitary transformations for a respective qubit (i.e., a respective system qubit) of the third plurality of qubits may be a neighboring ancillary qubit or a neighboring system qubit. For example, auxiliary ancillary qubit 2a in Figures 3A and 3B is neighboring system qubit 3a and may be used to control the unitary operation for system qubit 3a.

[0056] The next step in this disclosure is to calculate the inverse rotation transformation R about the rotation axis z. z 6, the inverse rotation transform R(-θ / n);95 may be applied 860 to each of the qubits, where the inverse rotation transform may be defined as a fraction θ / n of a given rotation angle about a rotation axis z (i.e., the same angle θ / n is used for the rotation transform). z (-θ / 2) can be defined by half the predetermined rotation angle θ / 2;90 about the rotation axis z. In a next step, the method can include applying 870 a CNOT operation 10 to each qubit and to a qubit from one or more qubits adjacent to said each qubit that is used to control one or more unitary transformations for the respective qubit (this second CNOT operation is an inverse rotation transformation R z(-θ / 2)) to the respective qubits. For example, if the control qubit, an ancillary qubit shown in FIG. 6, is in the zeroth quantum state |0〉 (e.g., after the initialization step disclosed further above), the corresponding quantum state of the respective qubit remains unchanged when the two CNOT operations are applied. Thus, each qubit (i.e., each system qubit in FIG. 6) is rotated back and forth by a predetermined rotation angle θ / n after applying the two rotations and two CNOT operations described above. The result of these four operations can be expressed as Rz(θ / n)Rz(-θ / n)=I, where I represents the identity operator (e.g., represented by a 2×2 unit matrix). On the other hand, if the control qubit is in the first quantum state |1〉 (e.g., after the initialization step), the quantum state of the respective qubit can be inverted with each CNOT gate. For example, the superposition quantum state of each qubit can be

number

number

[0057] The next step of the technique is to determine whether, when a qubit from one or more qubits used to control one or more unitary transformations for a respective qubit is in a corresponding quantum state (e.g., a first quantum state |1〉), the resulting rotation after using the combination of said rotation and CNOT operations is a rotation transformation R about a rotation axis z by a predetermined rotation angle θ. Z (θ) is equivalent to applying a rotation transformation R around the rotation axis z. Z (θ / n), CNOT operations on each qubit and from one or more qubits to each qubit, and an inverse rotation transformation R around the rotation axis z. Z Iteratively applying 880 a combination of (-θ / n) and a CNOT operation to each qubit and to the qubit from one or more qubits. For example, as described above in connection with the embodiment of FIG. 6, if the control qubit is in the first quantum state |1〉 (e.g., prepared in this state after an initialization step), each qubit is rotated by a predetermined rotation angle θ after applying the two rotations and two CNOT operations, and thus no further iterations are required. In some cases, e.g., for n>2, a fraction θ / n of a predetermined rotation angle about a predetermined axis a can be defined as the predetermined rotation angle divided by 2m, where m is any integer. In this case, the combination of rotations and CNOT operations can be applied iteratively 2m times to each qubit and to the qubit from one or more qubits, thereby rotating each qubit by a predetermined rotation angle θ when the control qubit is in the first quantum state |1〉. On the other hand, if the control qubit is in the 0th quantum state |0〉, then the corresponding quantum state of each qubit remains unchanged by applying this iterative procedure, as explained in detail above. In the next step, each qubit is subjected to the inverse basis rotation transformation

number

number

[0058] In some examples of the present technology, a controlled rotation transformation R a The one or more CNOT operations used for (θ);70 may be performed by respective quantum CNOT gates. Additionally or alternatively, the one or more CNOT operations may each include decomposing the one or more CNOT operations into corresponding quantum operations that are performed by native hardware gates, which are gates available in a particular architecture of a quantum computer and / or qubit topology, as further described above.

[0059] The techniques of the present disclosure may further include performing a quantum computing task, the quantum computing task including a plurality of quantum computing operations performed on one or more qubits (i.e., system qubits) of the third plurality of qubits. For example, the quantum computing task may include one or more problems in fields such as simulation of quantum systems, computational chemistry, computational biology, solid state physics, quantum annealing, quantum machine learning, search problems, cryptography, and the like. In some examples, the one or more quantum computing operations may be performed in parallel on different system qubits. For example, a first number of operations may be performed sequentially on a first number of system qubits in parallel with a second number of operations that are performed sequentially on a second number of system qubits during a first time interval. In some cases, a first number of qubits (i.e., ancilla qubits) of a first one or more qubits used to control the first number of system qubits can be initialized and / or predetermined information content (e.g., their quantum state) can be sent to the first number of system qubits in parallel with performing a second number of operations on the second number of system qubits during a second time interval (which may be equal to or different from the first time interval). Thus, the techniques of this disclosure can further reduce computation time compared to some prior art approaches that do not use auxiliary ancilla qubits and, as a result, are unable to take advantage of parallel operations in the sense described above.

[0060] A second aspect provides a quantum computing system 1000 configured according to any of the steps of the technique according to the first aspect.

[0061] The third aspect provides a quantum computing system 1000 for performing controlled quantum computation operations and adapted to perform any of the steps of the technique according to the first aspect. In some examples, the quantum computing system of the third aspect is configured according to the quantum computing system of the second aspect. The present disclosure also relates to a computer program adapted to perform any of the steps of the technique according to the first aspect. The present disclosure also relates to a computer-readable medium (e.g., a machine-readable storage medium such as an optical storage medium, or a read-only memory, e.g., a flash memory), and a signal storing or encoding a computer program of the present disclosure.

[0062] A quantum computing system of the second and / or third aspect may include at least one processor (e.g., a quantum processor), at least one memory (which may include a program that, when executed, executes the method steps or computer program according to the first aspect of the disclosure), and at least one interface for input / output. In some examples, the quantum computing system may comprise a hardware architecture comprising, for example, one or any combination of one or more chips, a quantum data plane, a control plane, a measurement plane, a control processor plane, a host processor, etc. The hardware architecture of the quantum computing system of the second and / or third aspect may be based on qubits coupled to high finesse resonators (e.g., superconducting qubits coupled to microwave cavities), as further described above. In other examples, the quantum computing system may comprise a hardware architecture based on qubits realized as nuclear spin states of donor atoms embedded in respective host lattices. In yet other examples, the quantum computing system may comprise a hardware architecture based on neutral atoms in an optical lattice. In some examples, the quantum computing system may be a standalone computing device. In other examples, the quantum computing system may be integrated into a computing device or system that also serves other purposes besides performing the steps of the techniques of the present disclosure. In yet other examples, the quantum computing system may be a distributed system that communicates over a network (e.g., the Internet).

[0063] A fourth general aspect of the present disclosure relates to a remote computing system comprising a quantum computing system, the remote computing system being configured to perform a quantum computing task, the quantum computing task may include a plurality of quantum computing operations performed on respective qubits according to the first aspect. The plurality of quantum computing operations of the fourth aspect (performed by the remote computing system) may be controlled according to any of the method steps of the first aspect. In some examples, the remote computing system may be configured to receive a query regarding the quantum computing task from a computer-implemented system (e.g., external to the remote computing system). The remote computing system of the fourth aspect may be further configured to transmit results of the computation task (e.g., based on the plurality of controlled quantum computing operations performed on the system qubits) to the computer-implemented system (e.g., to the computer-implemented system from which the query originated). In some examples, the hardware architecture of the quantum computing system of the fourth aspect may comprise one or more building elements (or blocks of elements) of the hardware architecture of the quantum computing system from the second and / or third aspects above. In some cases, the hardware architecture of the quantum computing system of the fourth aspect may be the same as the hardware architecture of the quantum computing system from the second and / or third aspects above.

Claims

1. 1. A method of configuring a quantum computing system, the quantum computing system comprising a plurality of qubits arranged on a two-dimensional (2D) lattice; receiving (100) a selection of a first one or more qubits (15; 1a-1c) of the plurality of qubits, the first one or more qubits are configured to be initialized to a predetermined information content; receiving (200) a selection of a second plurality of qubits (16; 2a-2c) of said plurality of qubits, one or more qubits (2a; 2c) of the second plurality of qubits are adjacent to at least one qubit (1a; 1c) respectively of the first one or more qubits and are configured to receive the predetermined information content from the at least one qubit respectively of the first one or more qubits; receiving (300) a selection of a third plurality of qubits (17; 3a-3c) of said plurality of qubits configured to perform a plurality of quantum computing operations, a quantum computation operation of the plurality of quantum computation operations for each qubit of the third plurality of qubits is controlled using the predetermined information content from the respective at least one qubit of the first one or more qubits; each qubit (2a) from some of the second plurality of qubits is adjacent to at least one qubit (3a) of the third plurality of qubits; and and each qubit (3 a) of the third plurality of qubits adjacent to each qubit (2 a) from the some of the qubits of the second plurality of qubits is configured to receive the predetermined information content from the respective qubit.

2. The method, after performing the step of receiving the selection of claim 1, further comprises: initializing (400) each at least one qubit of the first one or more qubits to the predetermined information content; transmitting (500) the predetermined information content of the respective at least one qubit of the first one or more qubits to the one or more qubits of the second plurality of qubits adjacent to the respective at least one qubit of the first one or more qubits; transmitting (600) the predetermined information content of one or more qubits (2a; 2c) of the second plurality of qubits to each other qubit (2b) of the second plurality of qubits, wherein each other qubit of the second plurality of qubits is configured to receive the predetermined information content from the one or more qubits (2a; 2c) of the second plurality of qubits; transmitting (700) the predetermined information content of one or more qubits (2 a) of the some of the qubits of the second plurality of qubits to one or more neighboring qubits (3 a) of each of the third plurality of qubits; performing (800) a plurality of quantum computing operations on the one or more qubits (3a-3c) of the third plurality of qubits, wherein the plurality of quantum computing operations on the one or more qubits are controlled using the predetermined information content transmitted to the one or more qubits of the third plurality of qubits; 10. The method of claim 1, comprising controlling a quantum computing system comprising:

3. the first, second, and third pluralities of quantum bits form a corresponding number of chains on the two-dimensional lattice; the first one or more qubits extend in a first direction comprising one or more chains of qubits; the second plurality of qubits extends in a second direction different from the first direction; the second plurality of qubits comprises two or more unconnected chains of qubits; the third plurality of qubits comprises a plurality of concatenated chains of qubits; 10. The method of claim 1 , wherein each chain of the plurality of concatenated chains of the third plurality of qubits extends in one of the first and second directions.

4. The predetermined information content of the first one or more qubits includes information about a quantum state (|ψ〉) of the one or more qubits, the quantum state being one of the following: a quantum state of a single qubit, where the predetermined information content is associated with the single qubit of the first one or more qubits, the quantum state of the single qubit of the first one or more qubits may be a zeroth quantum state (|0〉), a first quantum state (|1〉), or a linear superposition (α|0〉 + β|1〉) of the zeroth quantum state and the first quantum state; a multi-qubit quantum state, where the predetermined information content relates to at least two qubits of the first one or more qubits, The multi-qubit quantum state is a tensor product state ( [Equation 15] ), or entangled state ( [0016] ) and The method of claim 2, wherein the method is one of:

5. initializing (410) the at least one qubit of each of the first one or more qubits to the quantum state; transmitting (510) information regarding the quantum state of one qubit of the respective at least one qubit of the first one or more qubits from the one qubit to a qubit of a corresponding chain of the two or more disjoint chains of the second plurality of qubits; the single qubit being adjacent to the one qubit of the respective at least one qubit of the first one or more qubits; transmitting (610) information about the quantum state from the single qubit in the corresponding chain of the two or more disconnected chains of the second plurality of qubits to a respective adjacent qubit in the chain; iteratively transmitting (620) the information from the respective neighboring qubit in the chain to a next qubit in the chain that is adjacent to the respective neighboring qubit, the next qubit in the chain being considered the respective neighboring qubit for a next iteration; Optionally, repeatedly transmitting the information in the corresponding chain of the two or more uncoupled chains of the second plurality of qubits is performed until the information is transmitted to several qubits in the corresponding chain of the two or more uncoupled chains. The method of claim 3 further comprising:

6. initializing one or more qubits in the corresponding chains of the two or more unconnected chains of the second plurality of qubits to the zero quantum state (|0>); 6. To perform the sending step (510, 610, 620) of claim 5, using several successive controlled NOT (CNOT) operations (10) between adjacent qubits of each of the two or more disconnected chains, optionally one or more CNOT operations from the several successive CNOT operations being performed by a respective quantum CNOT gate. The method of claim 5 further comprising:

7. 6. The method of claim 5, further comprising resetting (630) each of the one or more qubits of the second plurality of qubits to the zero quantum state (|0>) after performing one or more quantum computing operations of the plurality of quantum computing operations on the one or more qubits of the third plurality of qubits to which the respective one or more qubits of the second plurality of qubits transmitted the predetermined information content, and optionally, the resetting (630) comprises applying several successive CNOT operations (10) between adjacent qubits of each of the two or more disjoint chains.

8. initializing (415) at least two qubits each of the first one or more qubits to the quantum state; transmitting (515) information regarding the quantum states of each of the at least two qubits of the first one or more qubits from the qubits to a single qubit of a corresponding chain of the two or more disjoint chains of the second plurality of qubits; the single qubit being adjacent to one or more qubits of the at least two qubits of each of the first one or more qubits; transmitting (615) information about the quantum state from the single qubit of the corresponding chain to a respective neighboring qubit of the chain of the second plurality of qubits; iteratively transmitting (625) the information from each neighboring qubit in the chain to a next qubit in the chain that is adjacent to the each neighboring qubit, the next qubit in the chain being considered the each neighboring qubit for the next iteration; Optionally, repeatedly transmitting information in the corresponding chain of the two or more uncoupled chains of the second plurality of qubits until the information is transmitted to a plurality of qubits in the corresponding chain of the two or more uncoupled chains. The method of claim 3 further comprising:

9. The method further includes transmitting the predetermined information content to a qubit of the third plurality of qubits for which no neighboring qubit from the second plurality of qubits is available, the transmitting step comprising: transmitting the predetermined information content from a qubit of the one or more qubits of the some of the second plurality of qubits to a qubit of the respective adjacent one or more qubits of the third plurality of qubits by applying a SWAP operation to the qubit; transmitting the predetermined information content from the qubits of the respective neighboring one or more qubits of the third plurality of qubits to the qubits of the third plurality of qubits for which a neighboring qubit from the second plurality of qubits is unavailable by repeatedly applying several subsequent SWAP operations between neighboring qubits of the third plurality of qubits located between the qubits; repeatedly applying the number of subsequent SWAP operations is performed until the predetermined information is swapped to a qubit of the third plurality of qubits that is adjacent to the qubit of the third plurality of qubits for which a neighboring qubit from the second plurality of qubits is unavailable; transmitting the predetermined information content from a qubit of the third plurality of qubits adjacent to a qubit of the third plurality of qubits for which a neighboring qubit of the second plurality of qubits is unavailable to a qubit of the third plurality of qubits for which a neighboring qubit from the second plurality of information bits is unavailable; a qubit of the third plurality of qubits for which a neighboring qubit from the second plurality of qubits is unavailable is configured to receive the predetermined information content from a neighboring qubit of the third plurality of qubits; performing a plurality of quantum computing operations on the qubits of the third plurality of qubits for which no neighboring qubits from the second plurality of qubits are available under control of the transmitted predetermined information; The method of claim 2 further comprising:

10. performing the plurality of quantum computing operations (800) includes performing one or more controlled unitary transformations (810) applied to a respective qubit of the third plurality of qubits, thereby altering a quantum state of the respective qubit, the one or more unitary transformations for the respective qubit being controlled using the predetermined information content transmitted to the respective qubit; Optionally, performing the one or more controlled unitary transformations on each qubit of the third plurality of qubits comprises performing a controlled rotation transformation (R a 70), wherein the rotation transformation is defined by a predetermined rotation angle (θ) about a predetermined axis (a).

11. The controlled rotation transformation (R a (θ); 70) (820) Base rotation transformation (V a,z ) to the respective qubits (830), wherein the basis rotation transformation corresponds to rotating a predetermined axis (a) around a rotation axis (z) of the respective qubit; The rotation transformation (R z (θ / n) to the respective qubits (840), wherein the rotation transformation is defined as a fraction (θ / n) of the predetermined rotation angle about the rotation axis (z); applying a CNOT operation (10) to the respective qubit and to a qubit from the one or more qubits adjacent to the respective qubit that is used to control the one or more unitary transformations for the respective qubit; The inverse rotation transformation (R z (-θ / n); 95) to the respective qubits (860), wherein the inverse rotation transform is defined as the fraction (θ / n) of the predetermined rotation angle about the rotation axis (z); applying a CNOT operation (10) to the respective qubit and to the qubit from the one or more qubits adjacent to the respective qubit used to control the one or more unitary transformations for the respective qubit (870); When a qubit from the one or more qubits used to control the one or more unitary transformations for the respective qubit is in a corresponding quantum state, the rotation transformation (R z (θ / n)), the CNOT operation on each qubit and from the one or more qubits to the qubit, and the inverse rotation transformation (R z (-θ / n)) and the CNOT operation on the respective qubit and the qubit from the one or more qubits, such that the resulting rotation after using the combination of rotation and CNOT operation is the rotation transformation (R (-θ / n)) about the rotation axis (z) by the predetermined rotation angle (θ). z (θ / n)) (880) Each of the qubits is subjected to an inverse basis rotation transformation. [Equation 17] wherein the inverse basis rotation transformation corresponds to rotating the rotation axis (z) of each qubit back to the predetermined axis (a); Optionally, the fraction (θ / n) of the predetermined rotation angle about the rotation axis (z) is defined as the predetermined rotation angle divided by 2m, where m is any integer, and the combination of rotation and CNOT operation is repeatedly applied 2m times to the respective qubit and to the qubit from the one or more qubits. The method of claim 10, comprising:

12. 2. The method of claim 1, further comprising performing a quantum computing task, the quantum computing task comprising the plurality of quantum computing operations performed on the one or more qubits of the third plurality of qubits.

13. 13. A quantum computing system (1000) configured by the steps of the method according to any one of claims 1 to 12.

14. 13. A quantum computing system (1000) configured to perform controlled quantum computation operations and adapted to perform the steps of the method of any one of claims 2 to 12.

15. A remote computing system comprising a quantum computing system (1000), 13. Performing a quantum computing task comprising a plurality of quantum computing operations according to the method of claim 12, Execution of the quantum computing task, wherein the plurality of quantum computing operations are controlled according to the steps of the method of any one of claims 2 to 12; sending the results of said computational tasks to a computer-implemented system; and a remote computing system adapted to perform the steps of:

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