Polyqubit encoding for quantum information processing

Abstract

Polyqubit encodings for quantum information processing are provided. In an exemplary embodiment, a plurality of quantum objects is provided. Each of the plurality of quantum objects has at least four states. The at least four states have a first partition and a second partition distinct from the first. The first partition corresponds to a first qubit and the second partition corresponds to a second qubit. The first qubit and the second qubits are separately manipulable. A first pair of transitions is driven across one of the first or the second partitions in a first of the plurality of quantum objects, thereby applying a gate to the corresponding qubit in the first of the plurality of quantum objects. Various embodiments enable intra-object gates and enable state preparation and measurement on qubits without affecting other qubits in the same quantum object.

Description

POLYQUBIT ENCODING FOR QUANTUM INFORMATION PROCESSINGCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Application No. 63 / 543,414, filed October 10, 2023, which is hereby incorporated by reference in its entirely.STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] This invention was made with government support under Grant Numbers 2110421 and 191255, awarded by the National Science Foundation and under Grant Number W91 INF-20- 1-0037, awarded by the U.S. Army, Army Research Office. The government has certain rights in the invention.BACKGROUND

[0003] Embodiments of the present disclosure relate to quantum computation, and more specifically, to polyqubit encoding for quantum information processing.BRIEF SUMMARY

[0004] According to embodiments of the present disclosure, methods of quantum computation are provided. A plurality of quantum objects is provided. Each of the plurality of quantum objects has at least four states. The at least four states have a first partition and a second partition distinct from the first. The first partition corresponds to a first qubit and the second partition corresponds to a second qubit. The first qubit and the second qubits are separately manipulable. A first pair of transitions is driven across one of the first or the second partitions in a first of the plurality of quantum objects, thereby applying a gate to the corresponding qubit in the first of the plurality of quantum objects.

[0005] In various embodiments, a second pair of transitions is driven across one of the first or the second partitions in a second of the plurality of quantum objects, thereby applying a gate to the corresponding qubits in the first of the plurality of quantum objects and in the second of the plurality of quantum objects.

[0006] In various embodiments, the first pair of transitions and the second pair of transitions are driven simultaneously.

[0007] In various embodiments, the first pair of transitions are driven simultaneously.

[0008] According to embodiments of the present disclosure, methods of quantum computation are provided. A plurality of quantum objects is provided. Each of the plurality of quantum objects has at least four states. The at least four states have a first partition and a second partition distinct from the first. The first partition corresponds to a first qubit and the second partition corresponds to a second qubit. The first qubit and the second qubits are separately manipulable. A first transition is driven across the first and / or the second partitions in a first of the plurality of quantum objects, thereby applying a gate to the first and / or second qubits of the first of the plurality of quantum objects.

[0009] In various embodiments, the value of the first or second qubit of the first or second quantum object is measured without measuring the other qubit of that quantum object.

[0010] In various embodiments, each of the plurality of quantum objects is an atomic ion.

[0011] In various embodiments, each of the plurality of quantum objects is a neutral atom.

[0012] In various embodiments, at least one of the four states is a hyperfine state.

[0013] In various embodiments, at least one of the four states is a Zeeman state.

[0014] In various embodiments, the four states are selected from an optical- frequency / metastable-state / ground-state (omg) structure.

[0015] In various embodiments, the first pair of states are hyperfine states F = 1,2 and the second pair of states are clock states mF= —1,1.

[0016] In various embodiments, the first qubit and the second qubit are prepared in target values by optically pumping the first quantum object with polarization controlled light to produce an initial state \F = 2, mp= 2), and transferring the initial state by micro wave or stimulated Raman transitions according to the target values.

[0017] In various embodiments, the first or the second qubit is prepared in a target value by measuring that qubit and applying a gate to prepare the target value.

[0018] In various embodiments, measuring the value of the first or second qubit comprises: providing a co-trapped ancilla ion to the ion of the first and second qubit; cooling a target mode of motion of the ion of the first and second qubit using the co-trapped ancilla; applying a time-dependent AC Stark shift to the co-trapped ancilla ion and the ion of the first and second qubit; measuring the motional energy of the co-trapped ancilla ion.

[0019] According to embodiments of the present disclosure, devices for performing quantum computation are provided, comprising: a plurality of ion traps, the plurality of ion traps configured to retain a plurality of quantum objects, the quantum objects being atomic ions, wherein each of the plurality of quantum objects has at least four states, the at least four states have a first partition and a second partition distinct from the first, the first partition corresponds to a first qubit and the second partition corresponds to a second qubit, the first qubit and the second qubits are separately manipulable; and at least one laser source configured to drive a first pair of transitions across one of the first or the second partitions in a first of the plurality of quantum objects, thereby applying a gate to the corresponding qubit in the first of the plurality of quantum objects.

[0020] According to embodiments of the present disclosure, devices for performing quantum computation are provided, comprising: a plurality of optical traps, the plurality of optical traps configured to retain a plurality of quantum objects, the quantum objects being neutral atoms, wherein each of the plurality of quantum objects has at least four states, the at leastfour states have a first partition and a second partition distinct from the first, the first partition corresponds to a first qubit and the second partition corresponds to a second qubit, the first qubit and the second qubits are separately manipulable; and at least one laser source configured to drive a first pair of transitions across one of the first or the second partitions in a first of the plurality of quantum objects, thereby applying a gate to the corresponding qubit in the first of the plurality of quantum objects.BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

[0021] Fig. 1 illustrates an exemplary two-qubit encoding according to embodiments of the present disclosure.

[0022] Figs. 2A-B illustrate exemplary single qubit gates according to embodiments of the present disclosure.

[0023] Figs. 3A-E illustrate an exemplary two-qubit gate scheme according to embodiments of the present disclosure.

[0024] Fig. 4 illustrates an example polyqubit encoding in an atomic ion ground state manifold according to embodiments of the present disclosure.

[0025] Figs. 5A-B illustrate single qubits gates according to embodiments of the present disclosure.

[0026] Fig. 6 illustrates polyqubit two-qubit gates according to embodiments of the present disclosure.

[0027] Fig. 7 illustrates a intra-atomic polyqubit two-qubit gate according to embodiments of the present disclosure.

[0028] Fig. 8 illustrates an exemplary encoding for the omg structure in133Ba+according to embodiments of the present disclosure.

[0029] Figs. 9A-B illustrates exemplary omg single qubit gates according to embodiments of the present disclosure.

[0030] Figs. 10A-B illustrates exemplary omg two qubit gates according to embodiments of the present disclosure.

[0031] Fig. 11 illustrates an exemplary level scheme for metastable states according to embodiments of the present disclosure.

[0032] Fig. 12 illustrates the transfer of one internal qubit eigenstate to a Rydberg manifold according to embodiments of the present disclosure.DETAILED DESCRIPTION

[0033] Quantum information processors use quantum objects, such as atoms, superconducting circuits, electron and nuclear spins, etc., to house quantum information. Almost all currently used quantum information processors define, at best, one quantum bit (qubit) of information in each quantum object. Technical considerations currently limit the number of quantum objects that can be effectively used together. The present disclosure provides a means for encoding multiple qubits in each quantum object and for performing both intra- and inter-quantum object qubit operations (e.g., gates).

[0034] The present disclosure describes methods for selective state-preparation and measurement (SPAM) of each individual qubit stored in a quantum object without disturbing the information encoded in the others (a crucial capability for quantum error correction). Whereas an IV-atom processor utilizes a resource state space of size 2Nwhen using monoqubit encoding, switching to a poly-qubit encoding of p qubits per quantum object increases the state space to size 2pN. Since the states utilized for poly qubit encoding are already present in many of the quantum objects in present-day processors, the resource costassociated with this increase in the qubit number may prove to be a good bargain in the short to medium term.

[0035] A quantum bit (qubit) is the fundamental building block for a quantum computer. By analogy to classical bits which are used to store information in traditional computers (each bit is 0 or 1), qubits can occupy two distinct states labeled |0) and | 1), or any quantum superposition of the two states. In various applications, multiple qubits are entangled in order to build multi-qubit quantum gates.

[0036] Bits and qubits are each encoded in the state of real physical systems. For example, a classical bit (0 or 1) may be encoded in whether a capacitor is charged or discharged, or whether a switch is ‘on’ or ‘off’.

[0037] The term qudit (quantum digit) denotes the unit of quantum information that can be realized in a suitable d -level quantum system. The term qutrit may be used to denote the use of three states.

[0038] Quantum bits are encoded in quantum systems with two (or more) distinct quantum states. There are many physical realizations that may be employed. One example is based on individual particles such as atoms, ions, or molecules which are isolated in vacuum. These isolated atoms, ions, and molecules have many distinct quantum states that correspond to different orientations of electron spins, nuclear spins, electron orbits, and molecular rotations / vibrations.

[0039] In principle, a qubit may be encoded in any pair of quantum states of the atom / ion / molecule. In practice, a key parameter of qubits is described by their quantum coherence properties. Coherence measures the lifetime of the qubit before its information is lost. It has a close analogy with classical bits: if you prepare a classical bit in the 0 state, then after some time it may randomly be flipped to 1 due to environmental noise. Quantum mechanically, the same error may occur: |0) may randomly flip to | 1) after somecharacteristic timescale. However, qubits may suffer from additional errors: for example, a superposition state (|0) + | 1)) / 2 may randomly flip to (| 0) — | 1)) / V2. In real quantum computers, the qubits must be encoded in quantum states which have long coherence properties.

[0040] Quantum computers generally can contain many qubits, each encoded in its own atom / molecule / ion / etc. Beyond simply containing the qubits, the quantum computer should be able to (1) initialize the qubits, (2) manipulate the state of the qubits in a controlled way, and (3) read out the final states of the qubits. When it comes to the second of these, manipulation of the qubits, this is usually broken down into two types: one type of qubit manipulation is a so-called single-qubit gate, which means an operation that is applied individually to a qubit. This may, for example, flip the state of the qubit from 10) to 11), or it may take |0) to a superposition state (|0) + | 1)) / V2. The second necessary type of qubit manipulation is a multi-qubit gate, which acts collectively on two or more qubits, including those that are entangled. A multi-qubit gate is realized through some form of interaction between the qubits. The various quantum computing platforms (having various physical encodings of qubits) rely on different physical mechanisms both for single-qubit gates as well as multi-qubit gates according to the physical system that is storing the qubit.

[0041] In various embodiments of a quantum computer, a qubit is encoded in two near- ground-state energy levels of an atom, ion, or molecule. An example of this is a hyperfine qubit. Such a qubit is encoded in two electronic ground states that differ by the relative orientation of the nuclear spin with respect to the outer electron spin. Pairs of such states can be chosen so that they are particularly robust / insensitive to environmental perturbations, leading to long coherence times. These states are split in energy by the hyperfine interaction energy of the atom / ion / molecule, which is the interaction energy between the nuclear spin and the electrons. The robustness of the qubit against phase flips can be understood as theenergy splitting between the two states being particularly stable. For this reason, such states are called clock states because the stable energy splitting can form an excellent frequencyreference and as such forms the basis for atomic clocks. Typical hyperfine splitting between these qubit states is in the 0.1-20 GHz frequency range.

[0042] To perform single-qubit gates on such a hyperfine qubit, it is possible to apply coherent micro wave radiation at the exact frequency of the energy splitting between states. However, there are two drawbacks to this approach. First, microwaves cannot be applied to just one qubit without also being applied to adjacent qubits. This is because qubits are encoded in particles that are typically just a few microns apart from one another, and microwaves cannot be focused to such a small scale due to their large wavelength. Second, the microwave intensity is fairly limited and as such the maximum speed of single-qubit gates is correspondingly limited.

[0043] An alternative approach is based on stimulated Raman transitions. In this case, a laser field is applied to the atoms / ions / molecules. The laser field is nearly (but not exactly) resonant with an optical transition from one of the ground states to an optically excited state. The laser contains multiple frequency components separated in frequency by exactly the amount equal to the hyperfine splitting of the qubit. The atom / ion / molecule can absorb a photon from one frequency component and coherently emit into a different frequency component, and in doing so it changes its state. This approach benefits from the capability of focusing the laser field onto individual particles or subsets of particles in the quantum computer. The laser field can also be applied with high intensity, allowing much faster gate operations.

[0044] Neutral atom quantum computers encode qubits in individual neutral atoms. The neutral atoms are trapped in a vacuum chamber and levitated by trapping lasers. Most commonly, the trapping lasers are individual optical tweezers, which are individual tightlyfocused laser beams that trap an individual atom at the focus. Alternatively, individual atoms may be trapped in an optical lattice, which is formed from standing waves of laser light which produce a periodic structure of nodes / antinodes.

[0045] A typical approach for encoding a qubit in neutral atoms is the hyperfine qubit approach, in which two ground states split by several GHz form the qubit. Multi-qubit gates in neutral atom quantum computers are realized using a third atomic state, which is a highly- excited Rydberg state. When one atom is excited to a Rydberg state, neighboring atoms are prevented from being excited to the Rydberg state. This conditional behavior forms the basis for multi-qubit gates, such as a controlled-NOT gate. The Rydberg state is used temporarily to mediate the multi-qubit gate, and then the atoms are returned back from the Rydberg state to the ground state levels to preserve their coherence.

[0046] Trapped ion quantum computers use atomic species that are ionized, meaning they have a net charge. In most cases, many ions are trapped in one large trapping potential formed by electrodes in a vacuum chamber. The ions are pulled to the minimum of the trapping potential, but inter-ion Coulomb repulsion causes them to form a crystal structure centered in the middle of the trapping potential. Most commonly, the ions arrange into a linear chain. Other ways to trap ions are also possible, such as using optical tweezers, or trapping ions individually with local electric fields with a more complex on-chip electrode structure.

[0047] Qubits are encoded in trapped ions in multiple ways. One common approach is to use ground- state hyperfine levels, as described for neutral atoms. In trapped ions with hyperfine- qubit encoding, as with neutral atoms, single-qubit gates may use microwave radiation or stimulated Raman transitions.

[0048] Unlike in neutral atoms, trapped ion hyperfine qubits rely heavily on stimulated Raman transitions for performing multi-qubit gates. Stimulated Raman transitions may beused to control both the hyperfine state of the ion but also to change the motional state of the ion (z.e., add momentum). This can be understood as absorbing a photon moving in one direction and emitting a photon in a different direction, such that the difference in photon momentum is absorbed by the ion. Since many ions are often trapped in one collective trapping potential and are mutually repelling one another, changing the motional state of one ion affects other ions in the system, and this mechanism forms the basis for multi-qubit gates.

[0049] According to various embodiments of a quantum computer, individual particles (atoms / ions / molecules) can first be trapped in an array and arranged into particular configurations. Next, one or more particles are prepared in a desired quantum state.Quantum circuits can then be implemented by a sequence of qubit operations acting on individual qubits (single-qubit gates) or on groups of two or more qubits (multi-qubit gates). Finally, the state of the particles can be read out in order to observe the result of the quantum circuit. The readout can be accomplished using an observation system that typically includes an electron-multiplied CCD (EMCCD) camera image to detect particles’ loaded positions, and a second camera image to read out the particles’ final states by, for example, detecting fluorescence conditionally emitted by the particles depending upon their final states.

[0050] If a quantum computation does not utilize the non-local nature of entanglement it is not necessary that the quantum information be encoded in distinct physical systems. In such a case, a quantum computation that requires n qubits can be performed in a single atom with N = 2nlevels. Performing a computation within a single atom has the advantage that the necessary quantum operations are all single-atom operations, which tend to have very high- fidelity. However, to fully access the states in the IV-atom Hilbert space requires O(N) controls, while an / V-dimcnsional Hilbert space composed of separate qubits needs only O(n) controls. Because of this scaling, it is clear that a scalable quantum computer cannot be constructed by simply using more and more levels of a single atom.- lo

[0051] Nonetheless, it is reasonable to expect that using more than just two levels of a given quantum system, i.e., a qudit, can provide benefit for quantum computation. While the future of quantum computing with qudits is a topic of much ongoing theoretical work, current quantum hardware overwhelmingly employs traditional qubits. This is in large part due to two facts. First, controlling even two levels in a quantum system can be challenging and the extra complexity required for qudit control is beyond current capabilities in many systems. Second, the vast majority of quantum algorithms are designed for one- and two-qubit operations.

[0052] The present disclosure addresses these challenges by showing how p qubits can be encoded into 2Pstates of a single quantum object. The present disclosure shows the design of controls that allow these qubits to be controlled, and measured separately, even though they are housed in the same quantum object. This allows algorithms designed for one- and two-qubit gates, as well as quantum error correction, to be employed on the system with a minimum of modification. This scheme also has the added benefit that intra-atom qubit ‘entangling’ gates are simply single quantum object operations, which can be performed with ultra-high fidelity.

[0053] As a concrete example, the present disclosure shows how two qubits can be encoded in four levels of an atom using currently available technology. Schemes are provided using current trapped atomic ion technology for this multi-qubit encoding. Additional examples are provided for neutral atom implementations, and it will be apparent that the present disclosure may be adapted to various other hardware implementations.

[0054] It will be appreciated that the present disclosure is teaching not qudits as understood in the art, but rather ways of encoding multiple qubits into the same quantum object in such a way that all of the operations (including SPAM) can be performed on arbitrarily chosen qubits or pairs of qubits without interfering with the others. An advantage of the presentdisclosure is that it increases the resource state space of the quantum computer (and thus its power) while still allowing current quantum algorithms, which are overwhelmingly designed for qubits not qudits, to be employed without modification. (Using a polyqubit encoding of p qubits per quantum object is equivalent in power to a qudit of dimensionality 2P.)

[0055] The present disclosure enables two-qubit inter-quantum-object operations and allows the use of current quantum algorithms to be used without modification. Moreover unlike qudit implementations, the present disclosure enables separately reading out multiple qubits from one quantum object without destroying the other.

[0056] Referring to Fig. 1, an exemplary two-qubit encoding is illustrated. Here, four states of a quantum system are used to encode two qubits. Note that three qubits would require 8 such states, while p qubits require 2Pstates.

[0057] The first index refers to qubit 1, defined on the upper (101) vs. lower (102) manifold in the image, while the second index refers to qubit 2, which is defined on the left (103) vs. right (104) manifolds in the image.

[0058] In the multiqubit encoding, quantum operations are used that separately affect each qubit. With such operations, quantum algorithms developed for qubits can run on the system without modification.

[0059] This is illustrated for single qubits gates in Fig. 2. Single-qubit gates can be driven by simultaneously driving (with matched Rabi frequencies) pairs of transitions corresponding to the appropriate degree of freedom. Specifically, V = can be implemented by drivingboth |00) 110) and |01) 111) (Fig. 2A). Likewise, V =canbe implemented bydriving |00) |01) and 110) 111) (Fig. 2B).

[0060] Inter-quantum-object gates are implemented in a similar manner. The native two- qubit gate of the system must be applied to both pairs of atomic states simultaneously to entangle that qubit with other quantum objects. These are shown schematically in Fig. 3,where arrows represent the internal states coupled in the entangling gate. As for single qubit gates, the relevant Rabi rates must be matched.

[0061] In each of these figures, two ions 301, 302 are illustrated, each embodying two qubits. As in Fig. 1, each first index refers to a first qubit, defined on the upper vs. lower manifolds, while each second index refers to a second qubit, which is defined on the left vs. right manifolds.

[0062] Whereas in Figs. 3A-D, inter-quantum object gates, Fig. 3E illustrates an intraquantum object gate. In this example, a single transition is driven between 100) and 111).

[0063] State detection can be done in a number of ways. If both qubits within a single quantum object are to be detected it is sufficient to simply do a projective measurement on the quantum object. Finding the quantum object in a single state then determines the value of both qubits. A variety of methods for this kind of state detection are known in the art for various hardware implementations. For state detection of only one of the qubits in a polyencoded quantum object, it is necessary to perform a measurement that collapses one qubit while leaving the other intact. The realization of such “weak” measurements varies between implementations and is discussed below for trapped atomic ions.

[0064] Ground- state atomic ion encoding

[0065] Referring to Fig. 4, an example polyqubit encoding in an atomic ion ground state manifold is illustrated. In particular, the electronic ground state manifolds F = 1,2 are associated with a first qubit and the quantum projection numbers mp= —1,1 are associated with a second qubit. Thus, a mapping is defined 100) -> F = 1, mp= — 1; 101) -> F = 1, mp= 1; 110) -> F = 2, mp= — 1; | 11) -> F = 2, mp= 1. It will be appreciated that alternative mappings to electronic ground states may be utilized in different atomic species.

[0066] An example polyencoding according to the present disclosure entails encoding two qubits into the ground-state manifold of a trapped ion. As an example, take137Ba+, whose I = 3 / 2 nuclear spin leads to total angular momentum F = 2 and F = 1 hyperfine manifolds in the electronic ground state. Any four of the eight mpsublevels in this hyperfine manifold can be used to encode the two qubits. For sake of illustration, the four |mF| = 1 states are chosen to define two qubits. The first qubit is denoted as |0) = \F = 1, i2) and |1) = |F = 2, i2) and the second qubitthis is a physical realization of the generalized up / down and left / right encodings discussed earlier.

[0067] To make this encoding work seamlessly with algorithms designed for qubits, it is necessary to be able to perform all quantum primitives for each qubit separately. This is a fundamental difference between using a qudit and a polyqubit encoding. Polyqubit encoding allows the use of current quantum algorithms, including quantum error correction, without any modification to the quantum circuit. The following details how to effect the required quantum primitives for each qubit separately.

[0068] Two-qubit state preparation for polyqubit encoding can be performed in a number of ways. For example, optical pumping with polarization-controlled light can produce the \F = 2, mp= 2) state which can be transferred by micro wave or stimulated Raman transitions to prepare any two-qubit state.

[0069] For state detection it is necessary to measure one qubit without disturbing the other. For a trapped ion, such a weak measurement in a polyencoded ion can be performed by, e.g., using a co-trapped ancilla ion as follows. First, the target mode of motion of the trapped ion crystal is cooled near its ground state using the ancilla ion. Next, a laser is used to apply a time-dependent AC Stark shift that adds energy to the system only if the target qubit is in a chosen state (which is encoded as the particular manifold identified with that state) by driving it with manifold- selective E2-E2 stark modulation. This step is done with equal strength andphase for the two manifolds of the spectator qubit within the ion. The ancilla ion can then be interrogated via laser-induced fluorescence to determine if the motional energy of the ions has increased, thereby performing a projective measurement on only one of the two qubits. In this way, state preparation of only the target qubits within a polyencoded atom can also be achieved without disturbing the spectator qubit.

[0070] Referring to Fig. 5, single qubits gates are illustrated for the qubit encoding of Fig. 4. Fig. 5A illustrates a single qubit gates for a first qubits and Fig. 5B illustrates a single qubits gate for a second qubit.

[0071] Single qubit rotations are performed by driving two transitions within the ion either sequentially or at once. This can be accomplished via, e.g., a two-tone microwave or stimulated Raman transition. The pulse area (Rabi rate X pulse duration) as well as the phase of the drive (in the interaction picture) on these two transitions must be matched, otherwise rotation on one qubit will affect the other (qubit cross -talk).

[0072] Referring to Fig. 6, polyqubit two-qubit gates are illustrated for the qubit encoding of Fig. 4. In this example, two ions 601, 602 are shown. The stimulated Raman laser polarization and frequency determines the qubit that participates in the gate.

[0073] Two qubit gates between distinct polyencoded ions are performed in a similar manner to two-qubit gates in monoencoded ions by adding tones to the drive to ensure the spectator qubits do not participate. As an example, the polarizations and frequencies of lasers used to drive stimulated Raman transitions can be chosen so that the desired two qubit gate is driven, shown in Fig. 6. Two-qubit intra-atom gates, on the other hand, are accomplished by simply driving a transition within the manifold.

[0074] For example, a CNOT gate may be applied by driving the 110) <-> |01) transition — i.e., the transition between \F = 2, mp= —1) <-> | = 2, mp+ 1). Alternatively, a more traditional CNOT mapping may be implemented by driving the 110) 111) transition.

[0075] Similarly, Fig. 7 shows how a Bell state can be prepared using a single transition, where an ion initially in 100) is driven by a TT / 2 pulse on the 100) <-> | 11) transition.

[0076] omg encoded polyqubits

[0077] Referring to Fig. 8, an encoding for the omg structure in1 33Ba+is illustrated. An omg structure is named after the three types of electronic qubits available: optical-frequency (o), metastable-state (m), and ground-state (g) qubits. These qubit types can be housed in a single ion species. The o qubit is composed of one ground state and one metastable state, with an energy splitting corresponding to an optical frequency. The m qubit is composed of two metastable atomic states, such as hyperfine or Zeeman levels, of an atomic2D / 2or2F° / 2state. In order to be useful for a qubit, such metastable states must have lifetimes that are long compared to the time quantum information is processed or stored in them, but they need not be as long as the lifetimes of g qubit states. The g qubit is composed of two very long-lived ground states (once again, hyperfine or Zeeman levels) of an atomic2S1 / 2state manifold. Interconversion between qubit types (type casting) is accomplished by driving transitions between ground and excited electronic states.

[0078] The omg structure is another example structure that is easily amenable to polyqubit encoding. For example, one qubit (gm) is defined as being in the upper or lower hyperfine manifold, while the other is defined as being in the upper or lower electronic state (o).

[0079] Here, two-qubit state preparation in a polyencoded atom can be accomplished by, e.g., optical pumping into the 100) state and using coherent transfer to other desired states. Measurement of individual qubits, as well as preparation of individual qubits, within a polyencoded atom can be accomplished without disturbing any spectator qubits in several ways, including the state-dependent heating previously discussed for ground state polyqubit encodings.

[0080] Effecting the quantum primitives is essentially the same as for ground state qubits.For single qubit gates, two transitions are driven with equal pulse area (and phase, in the interaction picture). For the hyperfine split qubits (gm), those transitions are via microwave or via stimulated Raman. For the optical qubit (o), the transitions are driven by a narrowband laser.

[0081] Fig. 9 illustrates omg single qubit gates.

[0082] Inter-ion two qubit gates in omg polyencoded ions proceed similarly to the procedure for ground state poly encoded ions. The two qubit gate for the hyperfine qubit is driven by stimulated Raman transitions, while the optical qubit is driven by the narrowband clock laser — e.g., Molmer-Sorensen or phase shift gate.

[0083] Fig. 10 illustrates omg two qubit gates.

[0084] Metastable atomic states

[0085] Metastable electronic states of trapped atomic ions provide another natural setting for defining poly qubit encodings. In this example, the specific case of Yb+in the long-lived metastable2F° / 2state is considered, but the same ideas work for more common systems such as metastable2D5 2states in the trapped alkaline earth ions.

[0086] Referring to Fig. 11, an exemplary level scheme for metastable states is provided. As in Fig. 1, four energy eigenstates are highlighted and labeled with two indices. The first index refers to qubit 1, defined on the upper vs. lower manifold in the image, while the second index refers to qubit 2, which is defined on the left vs. right manifolds in the image. It is assumed that there is a static magnetic field that shifts each of the four states by slightly different amounts so that the transition frequencies between all pairs are unique.

[0087] Single-qubit gates can be driven by simultaneously driving (with matched Rabi frequencies and phases in the interaction picture) pairs of transitions corresponding to the appropriate degree of freedom. Specifically, V = can be implemented by driving both|00) <-> 110) and |01) <-> 111). Likewise, V =canhe implemented by driving |00) <-> |01) and |10) |11).

[0088] Intra-atomic two-qubit gates can be built as described in the previous sections on ground state and omg qubits. Compared to inter-atomic two-qubit gates, this exhibits higher fidelity and speed since there is no coupling to motion required, which is also true of the ground state and omg poly encoded qubits.

[0089] For inter-atomic two-qubit gates, coupling to motion is employed. For coupling a single ion that hosts two qubits to motion, the desired qubit is coupled to motion while remaining agnostic to the state of the other. This is achieved by applying a time-dependent AC Stark shift via a laser whose light is close to (but not exactly on) resonance that couples the target qubit states to another state via an electric quadrupole (E2) transition. The E2-E2 stark shift is modulated close to resonance with a phonon mode of the trapped ion crystal, either only for one of the target qubit's eigenstate manifolds or with equal strength but opposite phase for the two eigenstate manifolds. This implements a ZZ gate between two qubits in distinct ions.

[0090] For state detection of only one of the qubits in a polyencoded ion, a co-trapped ancilla ion is used for readout as follows. First, the target mode of motion is cooled near its ground state using the ancilla ion. Resonant qubit-motion coupling of the E2-E2 type described above can add motional energy only if the target qubit is in the particular manifold that is driven by the E2-E2 stark modulation. The ancilla ion is then interrogated via laser-induced fluorescence to determine if the motional mode's energy has been increased.

[0091] Alternatively, a ZZ gate can be implemented between the target ion's qubit and an ancilla qubit prepared in a qubit eigenstate.

[0092] Rydberg (neutral) atoms

[0093] As described above, protocols are provided herein to perform State Preparation And Measurement (SPAM) of one target qubit in a polyencoded atom without disturbing the spectator qubit and to perform interatomic 2-qubit gates on arbitrary, individual qubits held in polyencoded atoms (again without disturbing the spectator qubits in those atoms). These features may be achieved with neutral atoms in a Rydberg processor as follows. Polyqubit encoding and intraatomic gates can be done as in ions, where for example the hyperfine and Zeeman structure of a ground or metastable state can have 4 states that are long lived in which two internal qubits may be stored.

[0094] Fig. 12 illustrates the transfer of one internal qubit eigenstate to a Rydberg manifold. Here, the polyqubit encoding is defined in the metastable nsnp3P2° electronic manifold as a combination of hyperfine and Zeeman sublevels for a species with nuclear spin I = 1 / 2. The coupling shown operates on the first of the two internal qubits, but this can be readily adapted for the second. Only one of the hyperfine states is shown for the Rydberg nsnrs3S1electronic manifold.

[0095] First, much like the case with ions, there is a co-trapped atom (which may be referred to as a SPAM atom) that can be queried for fluorescence without disturbing the data atoms, either by introducing a second species or using the omg blueprint. The SPAM atom is within a mutual-blockade radius of the data atom being queried during the SPAM protocol. For SPAM, the SPAM atom is first initialized into an X eigenstate of its ground state qubit.

[0096] To perform readout of only one of these qubits in a desired data atom, state- selective transfer of both energy eigenstates that correspond to a pre-selected (but arbitrary) qubit eigenstate of the qubit to be measured will move that population into two sublevels, |r0) and |rx), of a long-lived Rydberg state via simultaneous or sequential TT pulses. A subsequent state- selective 2TT pulse on the SPAM qubit will flip the sign of its superposition state iff the data atom is not in any Rydberg state. A subsequent 7T-pulse on the two Rydberg-transfertransitions (with a phase shift of n relative to the initial transfer) will return the data atom to its original encoding. Subsequent readout of the SPAM atom in the X basis will reveal the state of the target qubit on the data atom without disturbing the spectator qubit. This protocol can be used to measure the target qubit only, but state preparation can proceed by executing this entire sequence, then performing the desired rotation on the target qubit from its now- known initial state.

[0097] All of this relies on the existence of a mutual blockade between the data and SPAM atoms, the presence of which has been identified even for different elements.

[0098] For interatomic 2-qubit gates, the standard Rydberg blockade controlled phase gate can be modified by making the steps that drive transitions to Rydberg states occur with two frequencies instead of one, where the pulse areas of the TT pulses coupling each of the two energy eigenstates to individual levels in the Rydberg state are equal.

[0099] While several of the examples above focus on atoms, it will be appreciated that a poly qubit encoding may be employed with alternative quantum objects. For example, rotational and vibrational degrees of freedom of molecules are amenable to polyqubit encodings, where e.g., each vibrational mode could be used as a qubit.

[0100] It will be appreciated that the present disclosure provides various methods for polyqubit encoding in which multiple qubits in a single quantum object may be addressed, manipulated, and measured separately from each other. Accordingly, two qubits are referred to as separately manipulable when they can be manipulated individually, for example owing to the differences in frequency or polarization of the manipulation fields required for each.

[0101] In the various examples, multiple states of a quantum object are used to realize a polyqubit encoding. These states may be said to have multiple partitions with respect to the individual properties defining the states. Thus, to take the example of Fig. 4, there is a partition between F = 2 and F = 1, which corresponds to a first qubit and a partitionbetween mF= — 1 and mF= 1, which corresponds to a second qubit. The transitions depicted in Figs. 5A-B are said to be across a partition because they are between F = 2 and F = 1 in the first instance and mF= — 1 and mF= 1 in the second instance.

[0102] The descriptions of the various embodiments of the present disclosure have been presented for purposes of illustration, but are not intended to be exhaustive or limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terminology used herein was chosen to best explain the principles of the embodiments, the practical application or technical improvement over technologies found in the marketplace, or to enable others of ordinary skill in the art to understand the embodiments disclosed herein.

Claims

CLAIMSWhat is claimed is:

1. A method of performing a quantum computation, comprising: providing a plurality of quantum objects, each of the plurality of quantum objects having at least four states, the at least four states having a first partition and a second partition distinct from the first, the first partition corresponding to a first qubit and the second partition corresponding to a second qubit, the first qubit and the second qubits being separately manipulable; driving a first pair of transitions across one of the first or the second partitions in a first of the plurality of quantum objects, thereby applying a gate to the corresponding qubit in the first of the plurality of quantum objects.

2. The method of Claim 1, further comprising: driving a second pair of transitions across one of the first or the second partitions in a second of the plurality of quantum objects, thereby applying a gate to the corresponding qubits in the first of the plurality of quantum objects and in the second of the plurality of quantum objects.

3. The method of Claim 2, wherein the first pair of transitions and the second pair of transitions are driven simultaneously.

4. The method of any one of Claims 1 to 3, wherein the first pair of transitions are driven simultaneously.

5. A method of performing a quantum computation, comprising: providing a plurality of quantum objects, each of the plurality of quantum objects having at least four states,the at least four states having a first partition and a second partition distinct from the first, the first partition corresponding to a first qubit and the second partition corresponding to a second qubit, the first qubit and the second qubits being separately manipulable; driving a first transition across the first and / or the second partitions in a first of the plurality of quantum objects, thereby applying a gate to the first and / or second qubits of the first of the plurality of quantum objects.

6. The method of any one of Claims 1 to 5, further comprising: measuring the value of the first or second qubit of the first or second quantum object without measuring the other qubit of that quantum object.

7. The method of any one of Claims 1 to 6, wherein each of the plurality of quantum objects is an atomic ion.

8. The method of any one of Claims 1 to 6, wherein each of the plurality of quantum objects is a neutral atom.

9. The method of Claim 7 or 8, wherein at least one of the four states is a hyperfine state.

10. The method of Claim 7 or 8 wherein at least one of the four states is a Zeeman state.

11. The method of Claim 7 or 8, wherein the four states are selected from an optical- frequency / metastable-state / ground-state (omg) structure.

12. The method of Claim 7, wherein the first pair of states are hyperfine states F = 1,2 and the second pair of states are mp= —1,1.

13. The method of Claim 12, further comprising: preparing the first qubit and the second qubit in target values by optically pumping the first quantum object with polarization controlled light to produce an initial state\F = 2, mp= 2), and transferring the initial state by micro wave or stimulated Raman transitions according to the target values.

14. The method of Claim 12, further comprising: preparing the first or the second qubit in a target value by measuring that qubit and applying a gate to prepare the target value.

15. The method of Claim 7, wherein measuring the value of the first or second qubit comprises: providing a co-trapped ancilla ion to the ion of the first and second qubit; cooling a target mode of motion of the ion of the first and second qubit using the cotrapped ancilla; applying a time-dependent AC Stark shift to the ion of the first and second qubit; measuring the motional energy of the co-trapped ancilla ion.

16. A device for performing quantum computation, comprising: a plurality of ion traps, the plurality of ion traps configured to retain a plurality of quantum objects, the quantum objects being atomic ions, wherein each of the plurality of quantum objects has at least four states, the at least four states have a first partition and a second partition distinct from the first, the first partition corresponds to a first qubit and the second partition corresponds to a second qubit, the first qubit and the second qubits are separately manipulable; and at least one laser source configured to drive a first pair of transitions across one of the first or the second partitions in a first of the plurality of quantum objects, thereby applying a gate to the corresponding qubit in the first of the plurality of quantum objects.

7. A device for performing quantum computation, comprising: a plurality of optical traps, the plurality of optical traps configured to retain a plurality of quantum objects, the quantum objects being neutral atoms, wherein each of the plurality of quantum objects has at least four states, the at least four states have a first partition and a second partition distinct from the first, the first partition corresponds to a first qubit and the second partition corresponds to a second qubit, the first qubit and the second qubits are separately manipulable; and at least one laser source configured to drive a first pair of transitions across one of the first or the second partitions in a first of the plurality of quantum objects, thereby applying a gate to the corresponding qubit in the first of the plurality of quantum objects.

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