Systems and methods for parallel execution of multi-qubit quantum gates

Abstract

This provides a system and method for parallel execution of multi-qubit quantum gates. [Solution] The device includes a coherent light source configured such that, given a set of N qubits, where N is equal to 2 or greater; and selected values ​​for a set of parameters for at least first and second laser pulses, where the parameters are selected from relative phase shift, laser frequency, laser intensity and pulse duration, the first and second laser pulses are applied to all qubits in the set of N qubits, thereby coupling a non-interacting quantum state |1> to an interacting excited state |r>, and as a result, each qubit that starts in quantum state |1> returns to state |1> upon completion of at least the first and second laser pulses, and the qubits in the set are blocked from each other.

Description

[Technical Field]

[0001] Other references in related applications This application claims the benefit of U.S. Provisional Application No. 62 / 873,009, filed on 11 July 2019, which is incorporated herein by reference in its entirety. [Background technology]

[0002] background Any unitary operation can be performed on a quantum computer equipped with a complete set of universal gates. This complete set of gates can consist of single-qubit operations along with two-qubit controllable-NOT (CNOT) gates. CNOT gates have been demonstrated in several different physical systems, including trapped neutral atoms, trapped ions, superconducting circuits, and linear optics.

[0003] Quantum information processing using neutral atoms offers many intriguing opportunities. Neutral atoms can be captured in large numbers in flexible geometric structures using optical trapping techniques. Each individual atom can store qubit information at two hyperfine ground state levels |0> and |1>. Such storage has the advantages of high coherence times made possible by excellent isolation from the environment, near-perfect qubit initialization via optical pumping, individual optical readout of each qubit, and direct manipulation of a single qubit. Ultimately, strong, long-range interactions between atoms can be turned on by coupling to highly excited Rydberg states, enabling multi-qubit entanglement gates and making universal quantum computer computations possible.

[0004] Protocols for entangling atoms using Rydberg interactions have been investigated theoretically and experimentally over the past decade, but despite significant progress, advances in this field have been limited by the relatively low fidelity associated with ground-Rydberg state coherent control.

[0005] As described above, qubits encoded in the hyperfine state of a neutral atom can be entangled using controllable-phase (CZ) or CNOT gates mediated by Rydberg state interactions. A standard Rydberg-blocked CZ pulse sequence consists of a π pulse for the control qubit, a 2π pulse for the target qubit, and a π pulse for the control qubit, each pulse resonating between the ground hyperfine qubit state |1> and the Rydberg level |r>. If the control qubit enters the gate in state |1>, it is an excited Rydberg and occupies the Rydberg level (sit in) during the 2π pulse for the target qubit. Excitation and deexcitation of the target atom correspond to a 2π rotation of effective spin 1 / 2, and this thus imparts a π phase shift to the wavefunction of the target atom. If the control atom blocks the target excitation, no rotation occurs and there is no phase shift in the target wavefunction. The result is a CZ controllable-phase operation, where the phase shift of the target atom depends on the state of the control atom. Together with any single-qubit gate, this entanglement operation forms a universal quantum computer computation gate set. However, single-qubit addressing of multi-qubit quantum gates remains experimentally difficult because it requires applying local π and 2π pulses to the control and target atoms, respectively.

[0006] Therefore, there is a continuing need for improved systems and methods for implementing multi-qubit quantum gates. [Overview of the Initiative] [Means for solving the problem]

[0007] overview In an exemplary embodiment, the Disclosure provides a method for operating a quantum gate on a grouping of qubits, the method comprising the steps of: selecting values ​​for a set of parameters for at least first and second laser pulses, the parameters being selected from relative phase shift, laser frequency, laser intensity and pulse duration; and applying at least first and second laser pulses to all qubits in a group of N qubits, where N is equal to 2 or greater, thereby coupling a non-interacting quantum state |1> to an interacting excited state |r>, so that each qubit starting in quantum state |1> returns to state |1> upon completion of at least first and second laser pulses, and the qubits in the group are blocked from each other.

[0008] In another exemplary embodiment, the present disclosure provides a method for operating a quantum gate on a set of qubits, the method comprising the steps of: selecting time-dependent values ​​for a set of parameters of a laser pulse, where the parameters are selected from laser phase, laser frequency, laser intensity and pulse duration; and applying the laser pulse to all qubits in a set of N qubits, where N is equal to 3 or greater, thereby coupling a non-interacting quantum state |1> to an interacting excited state |r>, so that each qubit starting in quantum state |1> returns to state |1> upon completion of the laser pulse, and the qubits in the set are blocked from each other.

[0009] In yet another exemplary embodiment, the Disclosure provides a device comprising a set of N qubits, where N is equal to 2 or greater; and a coherent light source configured such that, given selected values ​​for a set of parameters for at least first and second laser pulses, where the parameters are selected from relative phase shift, laser frequency, laser intensity and pulse duration, at least first and second laser pulses are applied to all qubits in the set of N qubits, thereby coupling a non-interacting quantum state |1> to an interacting excited state |r>, so that each qubit starting in quantum state |1> returns to state |1> upon completion of at least the first and second laser pulses, and the qubits in the set are blockade of each other.

[0010] In another exemplary embodiment, the present disclosure provides a coherent light source comprising a set of N qubits, where N is equal to 3 or greater; and a laser pulse applied to all qubits in the set of N qubits, where selected time-dependent values ​​are chosen for a set of parameters of a laser pulse, where the parameters are selected from laser phase, laser frequency, laser intensity and pulse duration, thereby coupling a non-interacting quantum state |1> to an interacting excited state |r>, and as a result each qubit that starts in quantum state |1> returns to state |1> upon completion of the laser pulse, and the qubits in the set are configured to block each other.

[0011] The above system and method avoid the need to rapidly switch the laser between different spatial locations, and as a result have many advantages, such as enabling entangled gate operations on large qubit arrays and simultaneous operation of multiple gates on a collection of multiple separated atoms. [Brief explanation of the drawing]

[0012] Brief explanation of the drawing The various issues, features, and advantages of the disclosed subject matter can be better understood by referring to the following detailed description of the disclosed subject matter, in which similar reference figures identify similar elements. [Figure 1A] Figure 1A is a schematic diagram showing the relevant atomic levels used in exemplary embodiments of the systems described herein. [Figure 1B] Figure 1B is a schematic diagram showing the pairs of atoms used in exemplary embodiments of the systems described herein. [Figure 1C] Figure 1C is a plot of a Rabi oscillation from |0> to |1> driven by a Raman laser used in an exemplary embodiment of the system described herein. [Figure 1D] Figure 1D is a plot of the Rabi oscillation from |1> to |r> driven by a Rydeberg laser used in an exemplary embodiment of the system described herein. [Figure 1E] Figure 1E is a plot of local phase shifts for an addressed target atom and an unaddressed neighbor atom used in an exemplary embodiment of the system described herein. [Figure 2A] Figure 2A is a schematic diagram showing a pulse sequence used in an exemplary embodiment of the system described herein. [Figure 2B] Figure 2B is a schematic diagram showing the ground state used in exemplary embodiments of the system described herein. [Figure 2C] Figure 2C is a schematic diagram showing a two-level system used in exemplary embodiments of the system described herein. [Figure 2D] Figure 2D is a Bloch sphere representation of the pulse sequence for the two-level system shown in Figure 2C, used in exemplary embodiments of the system described herein. [Figure 2E] Figure 2E is a plot of the accumulated phase shown in Figure 2D as a function of detuning, used in exemplary embodiments of the systems described herein. [Figure 2F] Figure 2F is a schematic diagram showing another two-level system used in exemplary embodiments of the systems described herein. [Figure 2G] Figure 2G is a Bloch sphere representation of the pulse sequence for the two-level system shown in Figure 2F, used in exemplary embodiments of the system described herein. [Figure 2H] Figure 2H is a plot of the accumulation phase shown in Figure 2G as a function of detuning used in exemplary embodiments of the system described herein. [Figure 2I] Figure 2I is a schematic diagram showing the relevant atomic levels of a 3-qubit gate used in exemplary embodiments of the systems described herein. [Figure 2J] Figure 2J includes a Bloch sphere representation of a pulse sequence for the two-level system shown in Figure 2I, used in exemplary embodiments of the system described herein. [Figure 2K] Figure 2K includes a Bloch sphere representation of a pulse sequence for the two-level system shown in Figure 2I, used in exemplary embodiments of the system described herein. [Figure 2L] Figure 2L includes a Bloch sphere representation of a pulse sequence for the two-level system shown in Figure 2I, used in exemplary embodiments of the system described herein. [Figure 2M] Figure 2M includes a Bloch sphere representation of a pulse sequence for the two-level system shown in Figure 2I, used in exemplary embodiments of the system described herein. [Figure 2N] Figure 2N includes a Bloch sphere representation of a pulse sequence for the two-level system shown in Figure 2I, used in exemplary embodiments of the system described herein. [Figure 2O] Figure 2O includes a Bloch sphere representation of a pulse sequence for the two-level system shown in Figure 2I, used in exemplary embodiments of the system described herein. [Figure 3A] Figure 3A is a schematic diagram showing a quantum circuit used in an exemplary embodiment of the system described herein. [Figure 3B]Figure 3B is a plot of a measured population of computational ground states used in exemplary embodiments of the systems described herein. [Figure 3C] Figure 3C is a plot of parity oscillations as a function of accumulation phase used in exemplary embodiments of the systems described herein. [Figure 3D] Figure 3D is a schematic diagram showing a quantum circuit for a CNOT gate used in an exemplary embodiment of the system described herein. [Figure 3E] Figure 3E is a plot of the probabilities of four computational ground states used in exemplary embodiments of the system described herein. [Figure 3F] Figure 3F is a plot of the CNOT truth table used in exemplary embodiments of the system described herein. [Figure 4A] Figure 4A is a schematic diagram showing triplet-arranged atoms used in exemplary embodiments of the systems described herein. [Figure 4B] Figure 4B is a schematic diagram showing a quantum circuit for a Toffoli gate used in an exemplary embodiment of the system described herein. [Figure 4C] Figure 4C is a plot of the probabilities of eight computational ground states used in exemplary embodiments of the system described herein. [Figure 4D] Figure 4D is a plot of the Toffoli truth table used in an exemplary embodiment of the system described herein. [Figure 5A] Figure 5A is another schematic diagram showing the relevant atomic levels used in exemplary embodiments of the systems described herein. [Figure 5B] Figure 5B is a schematic diagram showing Raman-assisted optical pumping used in exemplary embodiments of the systems described herein. [Figure 5C] Figure 5C is a schematic diagram showing a quantum circuit used in an exemplary embodiment of the system described herein. [Figure 5D]Figure 5D is a schematic diagram showing a quantum circuit used in an exemplary embodiment of the system described herein. [Figure 5E] Figure 5E is a schematic diagram showing a quantum circuit used in an exemplary embodiment of the system described herein. [Figure 5F] Figure 5F is a schematic diagram showing a quantum circuit used in an exemplary embodiment of the system described herein. [Figure 5G] Figure 5G is a schematic diagram showing a quantum circuit used in an exemplary embodiment of the system described herein. [Figure 5H] Figure 5H is a schematic diagram showing a quantum circuit used in an exemplary embodiment of the system described herein. [Figure 5I] Figure 5I is a schematic diagram showing a quantum circuit used in an exemplary embodiment of the system described herein. [Figure 6] Figure 6 is a plot of the Rydberirabi frequency and detuning time variation used in exemplary embodiments of the systems described herein. [Figure 7A] Figure 7A is a schematic diagram showing a quantum circuit for a controllable-phase gate used in exemplary embodiments of the systems described herein. [Figure 7B] Figure 7B is a schematic diagram showing a pulse sequence used in an exemplary embodiment of the system described herein. [Figure 8A] Figure 8A is a schematic diagram showing measurement statistics for the CNOT and Toffoli truth tables used in exemplary embodiments of the systems described herein. [Figure 8B] Figure 8B is a schematic diagram showing measurement statistics for the CNOT and Toffoli truth tables used in exemplary embodiments of the systems described herein. [Figure 9] Figure 9 is a schematic diagram showing a quantum circuit for a Toffoli gate used in an exemplary embodiment of the system described herein. [Figure 10]Figure 10 is a plot of target probabilities for a tofoli gate used in an exemplary embodiment of the system described herein. [Figure 11A] Figure 11A is a schematic diagram showing another set of relevant atomic levels used in exemplary embodiments of the systems described herein. [Figure 11B] Figure 11B is a schematic diagram showing atoms arranged in pairs in a continuous chain of atoms used in exemplary embodiments of the systems described herein. [Modes for carrying out the invention]

[0013] Detailed explanation As used herein, the term “qubit” can refer to either the theoretical unit of information in a quantum computer or the physical implementation of the unit of a quantum circuit. In either case, the term typically refers to a two-level quantum mechanical system having two ground states denoted as |0> and |1>. While a classical “bit,” i.e., the theoretical unit of information in a conventional computer, can exist in one of two states denoted as “0” or “1,” a “qubit” can exist in any state that is a linear combination (superposition) of its two ground states. One example of a physical implementation of a quantum gate operated on two or more qubits involves an atom (or ion) that can be excited to a Rydberg state (i.e., a state with a very high value of principal quantum number n).

[0014] In some embodiments, this disclosure describes methods and systems for manipulating quantum gates with respect to a set of N qubits, where N is equal to 2 or more qubits. The methods and systems described herein may be applied to various qubits such as atomic qubits, ionic qubits, and molecular qubits. In one exemplary embodiment, a method is introduced for realizing a multi-qubit entangled gate between individual neutral atoms trapped in optical tweezers. The qubits are encoded into long-lasting hyperfine states |0> and |1>, which can be manipulated individually or collectively coherently to perform a single-qubit gate. A controllable-phase 2-qubit gate is performed using a protocol consisting of two global laser pulses driving neighboring atoms in a lyudebelli-blockade regime. As further described below, this gate, on average across five pairs of atoms, has high fidelity.

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[0015] According to one or more embodiments, individual 87Rb atoms are trapped by an optical tweezer and sorted into two or three groups by a real-time feedback procedure and arranged, for example, in a one-dimensional array. Qubits are encoded in the hyperfine ground states of these atoms, |0> = |5S 1 / 2 , F = 1, m F = 0> and |1> = |5S 1 / 2 , F = 2, m F = 0>. All qubits are initialized to |0> by a Raman-assisted optical pumping procedure described further below. Single-qubit coherent control is achieved by a combination of a global laser field that drives all qubits uniformly and a local addressing laser that applies an AC Stark shift to individual qubits. As shown in FIGS. 1A-1B, the global drive field 110 in device 100 is generated by a 795 nm Raman laser, which, as described further below, is tuned near the transition from 5S 1 / 2 to 5P 1 / 2 . This laser is intensity-tuned to generate a sideband that drives the qubits by a two-photon Raman transition using an effective Rabi frequency Ω 01 ≈ 2π × 250 kHz as shown in FIG. 1C. The local addressing beam 130 is generated by an acousto-optic deflector, which splits a single 420 nm laser tuned near the transition from 5S 1 / 2 to 6P 3 / 2 into several beams focused on individual atoms 131, producing an optical shift δ used for individual addressing. These two couplings from 5S 1 / 2 to 5P 1 / 2 and from 5S 1 / 2 to 6P 3 / 2 are described herein as a global X(θ) = exp(−iθX / 2) qubit rotation and a local Z(θ) = exp(−iθZ / 2) rotation, respectively. As described further below, after each sequence, the individual qubit states are measured by ejecting atoms in the |1> state from the trap using a resonant laser pulse and then taking a position-resolved fluorescence image of the remaining atoms.

[0016] The multi-qubit gate uses a bichromatic Rydberg laser 120 containing light at 420 nm and 1013 nm to transform atoms from the qubit state |1> to the Rydberg state |r> = |70S 1 / 2 , m J The atoms are manipulated by overall excitation to -1 / 2>. All atoms are uniformly coupled from a non-interacting quantum state |1> to an interacting excited state |r> via a two-photon process with detuning Δ and an effective Rabi frequency Ω ≈ 2π × 3.5 MHz, as shown in Figure 1D. Within a given cluster of atoms 131 and 132, the Rydberg interaction between nearest neighbors 131 and 132 is 2π × 24 MHz ≫ Ω; therefore, neighboring atoms 131 and 132 progress according to Rydberg blockade, and as a result, qubits 131 and 132 in the cluster are blocked from each other in such a way that they cannot be simultaneously excited to a Rydberg state. The protocol described herein may be applied to other mutually blocked qubits, such as dipole-blocked qubits. As shown in Figure 1E, the local phase shift measured in the Ramsey sequence averaged over the five atom pairs 131 and 132 shown in Figure 1B exhibits high contrast oscillation 135 for the addressed target atom 131 and limited (<2%) crosstalk 140 for the neighboring unaddressed atom 132.

[0017] To entangle atoms in such an array, a protocol is introduced herein for a (rely) 2-qubit controllable-phase (CZ) gate that relies solely on the overall excitation of atoms within a lyde-bell-blockade type. As shown in Figure 2B, the desired unitary CZ gate maps its computational ground state as follows: |00> → |00>, |01> → |01>e iφ , |10> → |10>e iφ , |11> → |11>e i(2φ-π) (1).

[0018] This map shows the canonical form of controllable-phase gates up to a single qubit phase φ.

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[0019] The gate can be understood by considering the behavior of the four computer-generated ground states. The |00> state is uncoupled by the laser field and therefore does not progress. The dynamics of |01> (and |10>) are that of a single atom

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[0020] Parallel operation of CZ gates is shown using CZ gates on pairs of five separate atoms, and is formalized using the quantum circuit shown in Figure 3A.

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[0021] The experimentally generated state ρ is the target Bell state.

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[0022] The measured Bell state fidelity includes errors in state preparation and measurement (SPAM), as well as errors in the two-qubit entangled gate. To specifically characterize the entangled gate, the error contribution from SPAM was evaluated (1.2(1)%) per atom, as further described below, and the SPAM corrected fidelity was also evaluated.

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[0023] Furthermore, the control of multiple atomic qubits is extended to execute a 3-qubit controlled-controlled-phase (CCZ) gate. This logical operation can be decomposed into five 2-qubit gates. Alternatively, this multiple-controlled gate is realized by directly preparing three atoms in a nearest-neighbor blockade configuration, where both outer atoms constrain the behavior of the intermediate atom. The complex 3-atom dynamics make it difficult to analytically construct a whole laser pulse that realizes the CCZ gate in this configuration. Therefore, numerical optimization is used to construct a whole amplitude and frequency modulated laser pulse that approximately performs the CCZ gate, as further described below. The laser pulse is optimized via a remote dressed chopped random basis (RedCRAB) optimal control algorithm.

[0024] As shown in Figure 4A, the CCZ gate is executed in parallel on four triplets of atomic qubits using the same laser as the two-qubit gate described above. The three atoms 410, 420, and 430 in each triplet are positioned so that their nearest neighbors (410, 420, and 420, 430) are blocked by a strong 2π × 24 MHz interaction, similar to the two-qubit execution. The edge atoms 410 and 430 interact weakly with each other (2π × 0.4 MHz). Similar to the two-qubit gate, the CCZ gate is embedded in a spin echo sequence to cancel out the optical shift, and the gate executes the CCZ with an overall X(π) rotation. The performance of this three-qubit gate is characterized by applying local Hadamard to the intermediate atom 420 before and after the CCZ gate (to simplify execution with the edge X(π) pulse, as shown in Figure 4B and further described below) to convert it to a Toffoli gate. The eight computer ground states are prepared with an average fidelity of 95.3(3)%, as shown in Figure 4C. The truth table fidelity corrected for SPAM errors is obtained by applying the Tofoli gate to each computer ground state, as shown in Figure 4D and further described below.

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[0025] These results can be directly improved and extended along several lines. The fidelity of Rydberg coupling is limited primarily by finite atomic temperature and off-resonant laser scattering, which can be addressed by sideband cooling of atoms in optical tweezers and higher-power lasers. Background atomic loss and state preparation can be improved using higher-quality vacuum systems and more refined state preparation techniques. Finally, atomic qubit readout can be improved using recently demonstrated non-destructive readout protocols to impose a stronger constraint on the atomic ensemble.

[0026] While parallel gate execution was performed herein for spatially separated clusters of atoms, the same approach can be extended to nonlocal coupling in continuous atom arrays using local addressing with further off-resonance laser systems. Specifically, subsets of the array can be simultaneously irradiated to generate optical shifts, which were then led to resonance using a globally resonant Rydberg-excited laser, as further described below. Furthermore, with more atoms arranged in blockade capacities, as further described below, the controllable phase gates presented herein can be extended to more multi-qubit gates with global coupling. Dipole interactions between S and P Rydberg states could also be used to achieve improved gate coupling between qubits. The combination of these results using recently demonstrated trapping and the rearrangement of individual neutral atoms in two-dimensional (2D) and three-dimensional (3D) arrays is well-suited for performing variability quantum optimizations with deep quantum circuits or hundreds of qubits. Furthermore, such a platform could be used to investigate efficient methods for error correction and fault-tolerant operations, ultimately enabling scalable quantum processing.

[0027] Raman laser The transitions between qubit states were driven using a 795nm Raman laser, which was red-detuned at 2π × 100GHz. 1 / 2 From 5P 1 / 2 This is the transition up to . The laser is coupled to a fiber-based Mach-Zehnder intensity modulator (Jenoptik AM785) that is DC-biased around the minimum transmission. The modulator is driven at half the qubit frequency (ω 01 Sidebands are generated at ±2π × 3.42 GHz (= 2π × 6.83 GHz), while the carrier and higher-order sidebands are strongly suppressed. This approach is passively stable on a 24-hour timescale without any active feedback, in contrast to other approaches that generate sidebands via phase modulation and then isolate the suppression of carrier modes using free-space engineering cavities or interferometers.

[0028] The Raman laser is aligned along an array of atoms (co-aligned with an 8.5G biased magnetic field), σ + With deflection, as shown in Figure 5A, the two sidebands coherently drive π transitions between F = 1 and F = 2 ground state manifolds using a Raman frequency of Ω = 2π × 250 kHz. The Raman driving light induces a differential optical shift of 2π × 20 kHz for qubit transitions, and the driving frequency of the intensity modulator is adjusted to correct this optical shift when a Raman pulse is applied.

[0029] Optical pumping to |0> The atom was subjected to |0>=|5S using a Raman-assisted pumping scheme with an 8.5G magnetic field. 1 / 2 , F=1, m F It is optically pumped to 0>. As shown in Figure 5B, |5S 1 / 2 F=1>All m in the manifold F The coarse pumping of atoms into a state is |5S 1 / 2 , F=2>~|5P 3 / 2The process begins by illuminating the resonant light for the transition F=2. Then, detuning is performed on the group |F=1, m F From =-1>, |F=2, m F A Raman π pulse is applied to drive the group to -1>. The second pulse drives the group to |F=1, m F = +1> from |F=2, m F This drives to |F=1> +1>. The process is then repeated by roughly pumping again any group moved to F=2, returning to the F=1 manifold. The net effect of one cycle is |F=1, m F = ±1>A portion of the group within |F=1, m F The process involves moving to 0. This cycle is typically repeated 70 times over a duration of 300 μs to achieve a 99.3(1)% |0> preparation fidelity.

[0030] Rydberg laser system The atoms are illuminated via a two-color laser system with wavelengths of 420 nm and 1013 nm, |1>=|5S 1 / 2 , F=2, m F =0> to |r> = |70S 1 / 2 , m J It is coupled to -1 / 2>. The laser is in the intermediate state |6P 3 / 2 > through σ - and σ + Each transition is deflected to drive the transition. |5S as the ground state level. 1 / 2 , F=2, m F In the previous execution using = -2>, the selection rule was |6P 3 / 2 It was confirmed that only a single intermediate sublevel and a single Rydberg state within the > can be coupled. Furthermore, the coupled two-photon transition was magnetically insensitive.

[0031] |1> = |5S 1 / 2 , F=2, m FThe coupling from 0 to the Rydberg state adds a little complexity, as described herein. First, several intermediate states are coupled, and both |70S within the Rydberg manifold. 1 / 2 , m J = ±1 / 2 > can reach sublevels. This is because m J To spectrally separate ±1 / 2 Rydberg levels, it is necessary to work in a higher magnetic field. In the embodiments described herein, a magnetic field of 8.5 G corresponds to 2π × 23.8 MHz m J = This results in separation between ±1 / 2. In the coupling from |1> to |r>, the matrix element is also reduced, while the laser scattering rate remains the same, and furthermore, the transition becomes magnetically sensitive here. Nevertheless, this scheme can be readily coupled with Raman laser systems and benefits from high-quality qubit states |0> and |1> in the ground state manifold that preserve coherence in optical tweezers. Although the sensitivity to the electric field does not change in this scheme, note that drifting or fluctuating the electric field can be constrained so that the Rydberg resonance changes only by less than 50 kHz.

[0032] One further complexity in this execution is another Rydberg state.

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[0033] Building quantum circuits from native single qubit gates All of the pulse sequences described above are broken down into pre-calibrated single-qubit gates (and, as shown above, globally, multi-qubit gates). The two single-qubit gates are X(π / 4), which is performed globally for all qubits simultaneously, and Z(π), which is performed by an optical shift from a laser focused on a single atom. In practice, the local Z(π) gate is applied simultaneously to one atom from each cluster (i.e., the leftmost atom in each cluster or an intermediate atom in each cluster).

[0034] Initialization of the computer's base state For two qubits, all four computer ground states are initialized using a global X(π / 2) pulse (consisting of two consecutive X(π / 4) gates) and a local Z(π) gate (the top qubit in each circuit) for only the left atom. The |00> state requires no pulse preparation, and the |11> state requires only the global X(π) gate. The |01> state is prepared as shown in Figure 5C, and the |10> state is prepared as shown in Figure 5D.

[0035] For the three qubits, the eight computer-generated ground states are reinitialized using X(π / 2) pulses and local Z(π) pulses that can be applied to any of the three atoms. |000> and |111> can each be re-prepared using either no operation or a global X(π) gate. The other states have one atom in |1> and the other two in |0> or vice versa. How both configurations are prepared is illustrated herein with two examples. Firstly, |100> is prepared as shown in Figure 5E. Secondly, the preparation of |110> requires local addressing to the rightmost atom, as shown in Figure 5F instead.

[0036] Local X(π / 2) for the CNOT gate

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[0037] Local Hadamard regarding Tofoli execution To convert the CCZ gate to a Toffoli gate, local rotations are applied to the target (intermediate) qubit before and after the CCZ pulse. The simplest way to achieve this given set of native gates is to apply global X(π / 4), then local Z(π), and then global X(3π / 4) to the intermediate qubit, as shown in Figure 5H.

[0038] For each end qubit, the net effect is simply an X(π) gate. For the intermediate qubit, this sequence continues with a Hadamard gate (defined along an axis different from the typical definition), where

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[0039] Design of a 2-qubit CZ gate This section provides a detailed theoretical discussion of the two-qubit gates implemented herein. The desired unitary operation maps the computational ground state as follows: |00> → |00>, |01> → |01> |10> → |10> |11> → |11>e iπ (3).

[0040] Up to the point of global gauge selection (i.e., global rotation of the qubit), this is equivalent to the following gate:

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[0041] To realize such a gate, both atoms are driven holistically and uniformly using a laser that couples state |1> to the Rydberg state |r>. This can be achieved via a single laser field or by a two-photon process. The Hamiltonian governing the dynamics of the atomic pair is:

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[0042] The dynamics of the system are decoupled into several simple sectors: (i) State |00> does not progress. (ii) If one of the atoms is in |0>, only the other systems progress. Thus the dynamics are given by states |1> = |a1> and |r> = |b1> and the Hamiltonian

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[0043] A controllable phase gate can be constructed from two identical pulses of a Rydberg laser field with equal duration τ and detuning Δ, along with a phase jump (i.e., relative phase shift) due to ξ in between. Each pulse alters the atomic state according to the unitary U = exp(-iHτ). The change in laser phase between pulses is Ω → Ωe iξ This effectively corresponds to driving the system around different axes on the Bloch sphere.

[0044] This explains the effect of both combined laser pulses.

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[0045] Next, consider the progression to state |11>, where all qubits in the set begin in quantum state |1>. Arbitrarily, the length or duration τ of each pulse is such that the system prepared in state |11> experiences a completely detuned Rabi oscillation, returning to state |11> after the first laser pulse; i.e.

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[0046] Finally, we consider the progression of states |01> and |10>. In each case, this progression can also be explained by detuned Rabi oscillations. However, due to the mismatch between the effective Rabi frequencies in H1 and H2, state |10> (|01>) does not return to itself after time τ, but a superposition state is generated: U|10> = cos(α)|10> + sin(β)e iγ |r0>, and U|01> = cos(α)|01> + sin(β)e iγ|0r>. The real coefficients α, β, and γ are determined by the selection of Ω, Δ, and τ. By appropriately selecting the phase jump (i.e., relative phase shift) between the first and second laser pulses ξ, it can always be ensured that the system returns to state |10>(|01>) after the second laser pulse. The phase jump is,

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[0047] Note that this construction can be generalized to multi-qubit controllable phase gates in well-blocked systems with more than two atoms, as will be further described below.

[0048] Accounting for incomplete blockade The above analysis is based on a complete blockade mechanism. Finite blockade interactions (and other imperfections such as coupling to other Rydberg states) can be accounted for, which may only result in a valid restandardization of the parameters given in equations (7-9). To refer to this, note that only finite values ​​of V affect the dynamics if the system is initially in state |11>. Instead of being limited to two states |a2> = |11> and |b2> = (|1r> + |r1>), a third state |c2> = |rr> must be considered, where H2 is,

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[0049] Experimental Calibration of the CZ Gate The CZ gate requires two laser pulses with a relative phase shift between them. The detuning Δ of the two pulses is determined by numerical calculation for experimentally calibrated Rydberg resonances. Both pulse time and phase jump between pulses require experimental calibration due to timing and phase perturbations associated with an acousto-optic modulator (AOM) based control system. The pulse time τ is initially calibrated by preparing both atoms in the qubit pair at |1> and driving them to a Rydberg state with detuning Δ. symmetrically excited states

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[0050] After fixing τ, only a single isolated atom is prepared to |1>, and two pulses of length τ are driven by a variable relative phase. The relative phase ξ is fixed by identifying the phase at which the single atom returns sufficiently to |1> by the end of the sequence.

[0051] Finally, the CZ gate (with a single-particle phase φ) in canonical form:

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[0052] This phase correction is performed by applying a total 420 nm laser at a fixed time in the absence of 1013 nm Rydberg light, which avoids any resonant Rydberg excitations and instead adds a phase shift. To calibrate the phase correction, a Bell state sequence is applied, where Bell state |Φ +An attempt is made to adjust >, and then a further X(π / 2) rotation is applied to both qubits. If the phase correction is optimal, the state |Ψ can be measured in the ensemble. + > should be prepared. Overall phase correction is performed at the end of this sequence |Ψ + >The program is modified to maximize the measured population within.

[0053]

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[0054] Execution of CCZ gate The above 2-qubit gate is,

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[0055] The dynamics of the three atoms contained are given by the Hamiltonian.

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[0056] In a configuration of three atoms where all three atoms are within the blockade radius, that is, all qubits in the assembly are mutually blocked, and as a result neither of the two atoms can be effectively excited to the Rydberg state at the same time, V i,j Let us consider what ≫ |Ω| ≫ |Δ| means. Next, the only difference from the above discussion of 2-qubit controllable phase gates is that there are two further levels that need to be considered here, where the state |111> = |e>,

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[0057] Using a sequence of pulses with scattered jumps (i.e., relative phase changes) in the laser drive phase,

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[0058] This pulse sequence is a generalization of the aforementioned 2-qubit pulse sequence, with p-cycles (of equal length, Rabi frequency, and detuning) and a p-1 relative change in the laser phase (without loss of generality). p The values ​​(= 0) are scattered. A controllable-controllable phase gate can be realized by a sequence of p = 6 pulses and a palindromic (e.g., symmetric) sequence of pulses, where ξ l = ξ p-l That is the case.

[0059] As used herein, the term “palindromic” refers to an ordered sequence of pulses that remains the same when the order is reversed. An example of a palindromic sequence of laser pulses is a “symmetric” sequence, i.e., a sequence of laser pulses that begins at time t = t0 and ends at time t = t1, characterized in that a plot of the amplitude of the laser light as a function of time A = A(t) exhibits reflection symmetry around the line t = 1 / 2(t1-t0).

[0060] The pulse length or duration can be changed again as desired.

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[0061] Three two-level systems, denoted A, B, and C, are shown in Figure 2I. The first pulses are shown as A10, B10, and C10 in Figures 2J-O. In Figures 2J-O, the notation X## is used, where the letters indicate two-level systems A, B, or C, the first digit indicates pulse numbers 1-6, and the second digit indicates phase shift numbers 1-5. The first pulse C10 is shown in system C in Figure 2I, as shown in Bloch sphere C10.

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[0062] Another version of this gate is V 1,2 , V 2,3 ≫ |Ω|, |Δ| and V 1,3 ≪ This can be constructed when atoms are arranged such that |Ω| and |Δ|. Using the same palindrome (e.g., symmetric) 6-pulse ansatz described by equation (19), where pulse length or duration τ is arbitrary,

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[0063] As described above, this controllable-controllable phase (CCZ) gate has its nearest neighbor bound by a lyudebell blockade, but the next nearest neighbor is V 1,2 , V 2,3 ≫ |Ω|, |Δ| and V 1,3 This is performed in a form with only weak interactions, such as |Ω| and |Δ|. Considering this, the CCZ gates performed are induced by the fact that the atoms at both ends can simultaneously block the intermediate (target) atom. In particular, the following scheme is thought to perform a CCZ involving local excitations to a Rydberg state:

[0064] 1. Apply a π pulse to the atoms at both ends to move all of those atoms in |1> to |r>. 2. A 2π pulse is applied to the central atom to excite it from |1> to |r> and back to |1>, and a π phase shift is accumulated only if none of the end atoms block this central atom and the atom is in |1>. 3. Apply another π pulse to the edge atoms to return any group from |r> to |1>. Such protocols are unitary:

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[0065] In the absence of local excitations to the Rydberg state, global Rydberg coupling can still be approximately realized as a unitary. Because different input configurations develop due to the dynamics of multi-level systems with different coupling frequencies, it is difficult to design a single analytical global pulse to appropriately control all input configurations. For example, the |001> state couples to |00r> as a two-level system with Rabi frequency Ω. The |011> state,

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[0066] To find an overall pulse that works for all input configurations, in one embodiment, the RedCRAB optimal control algorithm was used to optimize the amplitude and frequency profiles for the coupling field, thereby selecting the laser intensity, laser frequency, pulse duration, and laser phase. The optimized pulse shown in Figure 6 has a duration of 1.2 μs and achieves a desired numerically simulated gate fidelity of 97.6%.

[0067] Further executions using colder atoms could achieve higher gate fidelity by designing the gate timing to intentionally cancel out the effects of undesirable phase accumulation between the next nearest neighbors. Alternatively, some qubit gates could be performed using all atoms in a well-blocked form by bringing the atoms closer together or by exciting them to higher Rydberg states.

[0068] Spin echo procedure for CZ and CCZ The execution of the controllable phase gate within the enclosed region shown in Figure 7A is more clearly and in more detail to the right of the equals sign.

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[0069] State readout via atomic loss The primary technique used herein for state readout is to apply a resonant laser pulse to heat the atoms of |1> (more commonly F = 2) outside the tweezers, and then take a fluorescence image of the remaining atoms of |0>. This method accurately identifies the atoms of |0> but may miss atoms that have disappeared through background loss processes or due to residual Rydberg excitations for the atoms of |1>, resulting in an overestimation of the |1> population. For any measurement involving Rydberg excitations, the measurement statistics are recovered both with and without a pushout pulse to provide an upper bound on how much leakage occurred from the qubit subspace, and thus also a lower bound on the true population of |1>.

[0070] This procedure is illustrated with respect to a two-qubit experiment, with two types of measurements shown as A (|1> atom extrusion is applied) and B (extrusion is neutralized). For each measurement procedure, statistics were obtained by observing four two-qubit states consisting of "disappearance" or "presence" for each qubit. Since vector A is related to these as |0> and |1>, A ij (

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[0071] A ij and B ij both can be clearly expressed with respect to the basis atomic population p αβ where

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[0072] A ij and B ij when measured, where the target atomic population: p 00 p 01 p 10 and p 11 can be solved for.

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[0073] All probabilities are non-negative.

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[0074] This is an analysis performed on the Bell state set, the CNOT truth table, and the Toffoli truth table (extended to 3 qubits). For the truth tables, the analysis is performed on each measurement configuration (corresponding to different input computer ground states), shown separately as columns of the matrices in Figures 8A-B, and shows the probability distribution (shown as percentage points) of different output configurations with and without the push pulse, as described above.

[0075] Correction of condition adjustment and measurement errors The problem of correcting measured fidelity for state preparation and measurement (SPAM) errors is considered below. P is given as the probability of accurately initializing and measuring all qubits; generally,

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[0076] Experimentally, the SPAM error is

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[0077] Bell state fidelity The total probability that no error occurs for either of the two qubits is P = 97.6(2)%. Equation (47) holds for both collective measurements and parity oscillation measurements separately. Collective measurements only clearly count the lower bound on the population of atoms within the qubit subspace (see section: "State readout via atom loss" above). Therefore, when an atom is lost, there is no false contribution to the measured fidelity. However, the measured fidelity does not distinguish between atoms pumped to magnetic sublevels outside the qubit subspace. If one of the two atoms is prepared in an inaccurate magnetic sublevel (1.4(2)% probability),

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[0078] On the other hand, the parity oscillation amplitude is not affected by spurious contributions from cases where atoms are prepared or disappear at the wrong sublevel, because this error is independent of the accumulation phase and therefore does not oscillate as a function of the phase accumulation time. Therefore, the spurious contribution is

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[0079] CNOT truth table The truth table is measured by performing a CNOT gate on each computer ground state. The ground states are prepared with finite fidelity, as shown in Figure 3E. For each ground state, it is desirable to evaluate how well the gate performs this input state by evaluating how the finite output fidelity in the target state compares to the finite initialization fidelity. The probability P of no SPAM errors occurring for each measurement setting is... ij The state is established (where ij indicates the setting in which the computational ground state |ij> is initialized). Furthermore, the output in the target state is established.

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[0080] The spurious contribution to the measured fidelity is considered here. In the case where errors involved in atomic loss occur, since the fidelity measures only the atomic population within the qubit subspace, there is no spurious contribution to the fidelity. Alternatively, when an incorrect computer-based ground state is prepared,

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[0081] Toffoli truth table The same analysis is performed to evaluate the corrected Toffoli truth table fidelity for the CNOT truth table. As shown in Table 2 below, the average corrected truth table fidelity is

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Table 2

[0082] Limited tomography of the Toffoli gate The truth table of a Toffoli gate provides an indication of the scale of the matrix elements of the gate represented in the logical basis. However, the measured ensemble does not carry information about the relative phases between different entries. Performing a procedure similar to the truth table but rotating the Toffoli gate to act in the X basis instead of the Z basis makes it possible to recover some information about these phases. A limited version of such a procedure has been previously used as a way to characterize the fidelity of the Toffoli gate and is referred to as "limited tomography". The procedure consists of initializing all computational basis states in the Z basis in the quantum circuit shown in FIG. 9, and then applying X(±π / 2) rotations to all qubits before and after the Toffoli gate. The signs are chosen such that X(+π / 2) when the target qubit is initialized in |0>, and X(-π / 2) when the target qubit is initialized in |1>. Conditioning the sign of the rotation on the state of the target qubit forces the target qubit to always be in the same state |+> y before the operation of the Toffoli gate itself.

[0083] The Toffoli gate implemented herein, including the spin-echo pulse that acts as an overall X(π) gate (shown in FIG. 4B), has the unitary matrix:

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[0084] Performing the limited tomography procedure on this unitary results in the following output truth table:

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[0085] It is noteworthy that the limited tomography protocol uses only four of the eight X-basis input states, as can be seen from the fact that the target qubit is always initialized to |+>. This makes four of the eight measurements equivalent to the other four up to the overall X(π) rotation at the end. Comparing these two sets of measurements gives a constraint on the probability of leakage from the qubit subspace, similar to the approach described above in the section "State Readout via Atomic Vanishing".

[0086] Parallel gate execution in continuous arrays The above embodiment involves performing parallel multi-qubit gates on separate pairs of atoms, where the interaction between the pairs can be ignored. However, as illustrated in Figures 11A and 11B, this protocol can be extended to parallel gate execution on a continuous chain of atoms 1100. Consider, for example, a further local addressing laser system 1130 that can address any subset of atoms using an acousto-optic deflector. Specifically, the wavelength of this laser can be selected such that the allocated optical shift affects the |0> and |1> states equally, unlike the Rydberg state |r>. In such a case, as shown in Figure 11A, the optical shift from this further local addressing laser 1130 does not apply any qubit manipulation, but instead simply shifts the effective Rydberg resonance by δ. Near-infrared wavelength tuned away from any ground-state optical transition

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[0087] Using such a system, all pairs of adjacent atoms 1131 and 1132, intended to undergo a 2-qubit gate, can be irradiated, and then multi-qubit gates can be performed in parallel on all pairs by tuning the Rydberg laser to the optical shift resonance. The only constraint is that there must be sufficient space between the addressing pairs 1131 and 1132 so that their interaction (crosstalk) can be ignored in certain layers of gate execution.

[0088] Multi-qubit gate for a well-blocked ensemble of N qubits Consider a collection or assembly of well-blocked qubits (N=K) of N such that at most one qubit can be excited to a Rydberg state |r> simultaneously. The atomic qubit has two non-interacting qubit states |0> and |1> in addition to the interacting Rydberg state |r>. Under laser-driven operation coupling state |1> to state |r> using the Rabi frequency Ω and detuning Δ, the atomic ensemble progresses as an effective two-level system with an "enhanced" Rabi frequency, which depends on how many atoms start in the qubit state |1> (rather than |0>). There are N+1 such possible configurations, where the number of atoms starting in |1> (denoted by M) ranges from 0 to N. Each such system has an enhanced Rabi frequency

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[0089] The most common N-qubit gate that can be performed by the overall laser pulse protocol described herein is φ M Each of these N+1 configurations (labeled |M>, where M is 0 to N) includes a phase accumulation that returns them to their initial states. More specifically, if U is a unitary describing the operation of a gate, then each initial configuration |M> is:

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[0090] When designing a gate, a specific phase is:

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[0091] The laser pulse sequence Ansatz is defined to execute any target gate specified by the 2N-1 constraint. The sequence consists of 4N-6 laser pulses of each detuning Δ and duration τ, where the laser phase shift between each pulse is relative to the phase shift.

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[0092] Optionally, the pulse duration τ is selected such that one of the configurations |M> returns to its initial state after each laser pulse.

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[0093] Gate Phase

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[0094] As discussed above, for N = 2, Δ / Ω = 0.377371 and ξ1 = 3.90242. For N = 3, multiple solutions are observed, and four sample solutions are shown in Table 3. Note that solution 3 is the same solution discussed above, which is ξ2 + 2π and ξ3 + 2π. [Table 3]

[0095] For N = 4, multiple solutions were observed, and four sample solutions are shown in Table 4. [Table 4]

[0096] For N = 5, multiple solutions were observed, and two sample solutions are shown in Table 5. [Table 5]

[0097] Type C N-1 Z(π) gate(

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[0098] A CZ(π) gate on a single pair can be understood as adding a π phase shift to the ground state in which both qubits in the pair start at |1>, so the action of CZ(π) on all pairs in the system can be understood as adding a π phase shift to all pair formations of qubits in the ground state |1>. For the ground state |M> which is a superposition of all combinations of M qubits starting at |1>, the exact π phase shift of the qubits is

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[0099] Overall pulse with time-dependent intensity and detuning profile The most common pulses that can be described are laser pulses with a total duration T, a time-dependent intensity profile I(t), and a time-dependent detuning profile Δ(t), each defined for 0 ≤ t ≤ T, and consequently, the time-dependent values ​​of the laser intensity, laser frequency, laser phase, and pulse duration are arbitrarily selected based on a conditional phase angle θ. In principle, these profiles can be any function of time, but actual experimental limits set upper and lower bounds on the values ​​of the functions. For example, there is an actual limit on the maximum value of I(t) (how much laser power is available) and an actual limit on the range of Δ(t) (how far the laser can be smoothly detuned). Experimental limits also set boundaries on the continuity and smoothness of these functions or, equivalently, the frequency spectrum of these profiles. Some of the aforementioned limits on the high-frequency components (depending on the execution choice) are not experimentally achievable.

[0100] How did we find a way to execute a target gate within this limited (but still expansive) space of possible intensity and detuning profiles? One approach is to numerically simulate the behavior of the atomic system according to a given laser pulse (characterized by I(t) and Δ(t)), then optimize the laser pulse profile according to the simulated response of the system, thereby selecting the time-dependent values ​​of the laser intensity, laser frequency, pulse duration, and laser phase to achieve the desired fidelity of the quantum gate. In particular, starting from a fixed initial state |ψ0> for the atomic system, we can identify what is the ideal output state of the target gate. For example, the target gate is a unitary operator U ゲート It can be expressed as, in this case, the target output state is |ψ 標的 > = U ゲート The actual gate, executed by laser pulses with I(t) and Δ(t), is a numerically simulated output state |ψ sim > results in a performance index that characterizes how closely the simulated output state is to the target output state: fidelity

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[0101] Accordingly, in a first exemplary embodiment, the present invention is a method for operating a quantum gate on a set of qubits. In a first aspect of the first exemplary embodiment, the method includes the steps of: selecting values ​​for a set of parameters for at least first and second laser pulses, the parameters being selected from relative phase shift, laser frequency, laser intensity and pulse duration; and applying at least first and second laser pulses to all qubits in a set of N qubits, where N is equal to 2 or greater, thereby coupling a non-interacting quantum state |1> to an interacting excited state |r>, so that each qubit starting in quantum state |1> returns to state |1> upon completion of at least first and second laser pulses, and the qubits in the set are blocked from each other, for example, dipole blockade or rudebell blockade.

[0102] In the second aspect of the first exemplary embodiment, each qubit may be an atomic qubit, an ionic qubit, or a molecular qubit.

[0103] In the third aspect of the first exemplary embodiment, all qubits in the set are blocked from each other. Other features and exemplary features of the method are described above with respect to the first and second aspects of the first exemplary embodiment.

[0104] In the fourth aspect of the first exemplary embodiment, the durations of at least the first and second pulses are selected such that, if all qubits in the set begin in the quantum state |1>, then upon completion of at least the first and second laser pulses, all qubits in the set return to the quantum state |1>. For example, the laser frequency of each pulse is detuned by a detuning Δ from the resonant transition between |1> and |r>, and the pulse duration t is,

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[0105] In the fifth aspect of the first exemplary embodiment, one or more of the laser intensity, laser frequency, pulse duration, and laser phase are selected to achieve a desired fidelity of the quantum gate. Other features and exemplary features of the method are described above with respect to the first to fourth aspects of the first exemplary embodiment.

[0106] In the sixth aspect of the first exemplary embodiment, at least the first and second pulses form a palindromic sequence of pulses. Other features and exemplary features of the method are described above with respect to the first to fifth aspects of the first exemplary embodiment.

[0107] In the seventh aspect of the first exemplary embodiment, the gate is a controllable phase gate C N-1 Z(θ) is a conditional phase angle, for example, N=2. In another example, the quantum gate is a controllable phase (CZ) gate, and N=2. In yet another example, the laser frequency, pulse duration, and phase shift are selected based on the conditional phase angle θ of the controllable phase gate. In yet another example, the laser frequency is detuned by a detuning Δ from the resonant transition between |1> and |r>, and the laser intensity is selected such that the Rabi frequency of the laser pulse is Ω. For example, the laser frequency, laser intensity, pulse duration, and phase shift are selected such that the conditional phase angle θ=π. Other features and exemplary features of the method are described above with respect to the first to sixth aspects of the first exemplary embodiment.

[0108] In the eighth phase of the first exemplary embodiment, N is 3. In the eighth phase, the quantum gate has a controllable-controllable phase (C) with a conditional phase angle θ. 2It may be a Z(θ) gate. For example, the laser frequency, pulse duration, and phase shift of at least the first and second laser pulses are selected based on a conditional phase angle θ. Other features and exemplary features of the method are described above with respect to the first to seventh aspects of the first exemplary embodiment.

[0109] In the ninth aspect of the first exemplary embodiment, N is 3, and the method comprises applying a sequence of 6 pulses. The sequence of 6 pulses may be a palindrome. Other features and exemplary features of the method are described above with respect to the first to eighth aspects of the first exemplary embodiment.

[0110] In the tenth aspect of the first exemplary embodiment, the method includes applying a sequence of 4N-6 pulses. For example, the sequence of pulses may be a palindrome. Other features and exemplary features of the method are described above with respect to the first to ninth aspects of the first exemplary embodiment.

[0111] In a second exemplary embodiment, the present invention is a method for operating a quantum gate on a set of qubits. In the first aspect of the second exemplary embodiment, the method includes: selecting time-dependent values ​​for a set of parameters of a laser pulse, where the parameters are selected from laser phase, laser frequency, laser intensity and pulse duration; and applying the laser pulse to all qubits in a set of N qubits, where N is equal to 3 or greater, thereby coupling a non-interacting quantum state |1> to an interacting excited state |r>, so that each qubit that starts in quantum state |1> returns to state |1> upon completion of the laser pulse, and the qubits in the set are blocked from each other, for example, dipole blockade or rudebell blockade.

[0112] In the second aspect of the second exemplary embodiment, each qubit may be an atomic qubit, an ionic qubit, or a molecular qubit.

[0113] In the third aspect of the second exemplary embodiment, all qubits in the set are blocked from each other. Other features and exemplary features of the method are described above with respect to the first and second aspects of the second exemplary embodiment.

[0114] In the fourth aspect of the second exemplary embodiment, the time-dependent values ​​of the laser intensity, laser frequency, pulse duration, and laser phase are selected to achieve a desired fidelity of the quantum gate. Other features and exemplary features of the method are described above with respect to the first to third aspects of the second exemplary embodiment.

[0115] In the fifth aspect of the second exemplary embodiment, the gate is a controllable phase gate C N-1 Z(θ) is a conditional phase angle, where θ is a conditional phase angle. Other features and exemplary features of the method are described above with respect to the first to fourth aspects of the second exemplary embodiment.

[0116] In the sixth aspect of the second exemplary embodiment, N is 3. Other features and exemplary features of the method are described above with respect to the first to fifth aspects of the second exemplary embodiment.

[0117] In the seventh aspect of the second exemplary embodiment, N is 3, and the quantum gate has a controllable-controllable phase (C) with a conditional phase angle θ. 2 This is a Z(θ) gate. For example, the time-dependent values ​​of the laser intensity, laser frequency, laser phase, and pulse duration are selected based on a conditional phase angle θ. In another example, the conditional phase angle θ = π. Other features and exemplary features of the method are described above with respect to the first to sixth aspects of the second exemplary embodiment.

[0118] In a third exemplary embodiment, the present invention is a device. In one aspect of the third exemplary embodiment, the device includes a coherent light source configured such that: a set of N qubits, where N is equal to 2 or greater; and selected values ​​for a set of parameters for at least first and second laser pulses, where the parameters are selected from relative phase shift, laser frequency, laser intensity and pulse duration; at least first and second laser pulses are applied to all qubits in the set of N qubits, thereby coupling a non-interacting quantum state |1> to an interacting excited state |r>, so that each qubit starting in quantum state |1> returns to state |1> upon completion of at least the first and second laser pulses; and the qubits in the set are blockade of each other.

[0119] Other features and exemplary features of the third exemplary embodiment are described above with respect to various aspects of the first exemplary embodiment.

[0120] In a fourth exemplary embodiment, the present invention is a device. In one aspect of the fourth exemplary embodiment, the device includes a coherent light source configured such that: a set of N qubits, where N is equal to 3 or greater; and a set of time-dependent values ​​selected for a set of parameters for a laser pulse, where the parameters are selected from laser phase, laser frequency, laser intensity and pulse duration; the laser pulse is applied to all qubits in the set of N qubits, thereby coupling a non-interacting quantum state |1> to an interacting excited state |r>, so that each qubit starting in quantum state |1> returns to state |1> upon completion of the laser pulse, and the qubits in the set block each other.

[0121] Other features and exemplary features of the fourth exemplary embodiment are described above with respect to various aspects of the second exemplary embodiment.

[0122] While some exemplary embodiments are described herein, it will be understood that various modifications, alterations, and improvements will be readily apparent to those skilled in the art. Such modifications, alterations, and improvements are intended to form part of the disclosure and to be within the spirit and scope of the disclosure. While some examples shown herein involve specific combinations of functional or structural elements, it should be understood that these functions and elements may be combined in other ways by the disclosure to achieve the same or different purposes. In particular, actions, elements, and features discussed in one embodiment are not intended to be excluded from similar or other roles in other embodiments. Furthermore, elements and components described herein may be further divided into further components or combined to form fewer components to perform the same function. Accordingly, the foregoing descriptions and accompanying drawings are for illustrative purposes only and are not intended to be limiting.

Claims

1. A method for applying a quantum gate to two qubits containing neutral atoms, The steps include applying a first laser pulse to the two qubits using a first laser, After applying the first laser pulse, A step of applying a second laser pulse to the two qubits using the first laser, The second laser pulse has a phase shift ξ with respect to the phase of the first laser pulse. The first laser pulse and the second laser pulse are each applied to the two qubits for the same duration τ, in steps and A method that includes this.

2. A step of applying a third laser pulse to the two qubits using a second laser, simultaneously with applying the first and second laser pulses, wherein the third laser pulse is configured to be coupled with the first or second laser pulse to couple the qubit state |1> of one of the two qubits to a Rydberg state |r>. The method according to claim 1, further comprising:

3. Applying the first laser pulse or the second laser pulse includes applying a laser pulse with a wavelength of 420 nm. The method according to claim 2, wherein applying the third laser pulse includes applying a laser pulse with a wavelength of 1013 nm.

4. A step of using optical tweezers to position the two qubits at a distance from each other, wherein the distance is selected such that the two qubits block each other. The method according to claim 2, further comprising:

5. After applying the second laser pulse, The step of applying an overall X(π) echo pulse to the two qubits using a third laser. The method according to claim 2, further comprising:

6. The method according to claim 5, wherein applying the overall X(π) echo pulse to the two qubits includes applying four consecutive X(π / 4) pulses using the third laser.

7. The method according to claim 5, wherein applying the overall X(π) echo pulse to the two qubits using the third laser comprises applying the overall X(π) echo pulse to the two qubits using a Raman laser with a wavelength of 795 nm.

8. After applying the overall X(π) echo pulse, and using the second laser, without applying the laser pulse to the two qubits, A step of applying a fourth laser pulse and a fifth laser pulse using the first laser, wherein the fourth laser pulse and the fifth laser pulse are identical to the first laser pulse and the second laser pulse. The method according to claim 5, further comprising:

9. After applying the fourth laser pulse and the fifth laser pulse, The step of applying an additional phase correction to the quantum gate by applying a sixth laser pulse to the two qubits using the first laser. The method according to claim 8, further comprising:

10. The steps include capturing the two qubits using optical tweezers, The steps include turning off the optical tweezers while applying the first laser pulse and the second laser pulse, and while applying the fourth laser pulse and the fifth laser pulse. The method according to claim 8, further comprising:

11. The steps include selecting the period τ such that the first laser pulse yields a complete cycle of detuned Rabi oscillation when the two qubits are prepared as a |11> system, The step of selecting the phase shift ξ is to identify the phase at which one of the two qubits, after being prepared in state |1>, returns completely to state |1> after the first laser pulse and the second laser pulse are applied. The method according to claim 1, further comprising:

12. A system configured to apply a quantum gate to two qubits containing neutral atoms, The system comprises a first laser, the first laser being, Applying the first laser pulse to the two qubits, After applying the first laser pulse, Applying a second laser pulse to the two qubits, The second laser pulse has a phase shift ξ with respect to the phase of the first laser pulse. The first laser pulse and the second laser pulse are each applied to the two qubits for the same duration τ. A system configured to perform the following actions.

13. The system further comprises a second laser, the second laser being, The first laser applies the first laser pulse and the second laser pulse simultaneously with the application of a third laser pulse to the two qubits, wherein the third laser pulse is configured to be applied in combination with the first laser pulse or the second laser pulse to couple the qubit state |1> of one of the two qubits to a Rydberg state |r>. The system according to claim 12, configured to perform the following:

14. The first laser has a wavelength of 420 nm, The system according to claim 13, wherein the second laser has a wavelength of 1013 nm.

15. The optical tweezers are further equipped, and the optical tweezers are, The arrangement involves placing the two qubits at a distance from each other, such that the distance is selected to block the two qubits from each other. The system according to claim 13, configured to perform the following:

16. The system further comprises a third laser, the third laser being: After the second laser pulse is applied, Applying the overall X(π) echo pulse to the two qubits. The system according to claim 13, configured to perform the following:

17. The system according to claim 16, wherein the third laser has a wavelength of 795 nm.

18. The first laser, after the overall X(π) echo pulse has been applied to the two qubits, Applying a fourth laser pulse and a fifth laser pulse, wherein the fourth laser pulse and the fifth laser pulse are identical to the first laser pulse and the second laser pulse. The system according to claim 16, configured to perform the following:

19. The first laser is used after the fourth laser pulse and the fifth laser pulse have been applied to the two qubits. Applying a sixth laser pulse to the two qubits to apply additional phase correction to the quantum gate. The system according to claim 18, configured to perform the following:

20. The optical tweezers are further equipped, and the optical tweezers are, Capture each of the two aforementioned qubits, The two qubits are released from the optical tweezers while the first laser pulse and the second laser pulse are applied, and while the fourth laser pulse and the fifth laser pulse are applied. The system according to claim 18, configured to perform the following:

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