System and method for parallel implementation of multi-qubit quantum gates

Abstract

To provide a system and method for parallel implementation of multi-qubit quantum gates.SOLUTION: A method of operating a quantum gate on a grouping of qubits comprises: selecting values for a set of parameters of at least first and second laser pulses, the parameters are a relative phase shift between the at least first and second laser pulses, a laser frequency, a laser intensity and a pulse duration; and applying each of the at least first and second laser pulses to all qubits in the gate. The gate consists of a grouping of N qubits, where N is equal to two or more, thereby coupling a non-interacting quantum state |1> to an interacting excited state |r>. Each qubit that begins in the quantum state |1> returns to the state |1> upon completion of the at least first and second laser pulses, and all qubits in the grouping are mutually blockaded.SELECTED DRAWING: None

Description

[Technical field]

[0001] REFERENCE TO RELATED APPLICATIONS This application claims the benefit of U.S. Provisional Application No. 62 / 873,009, filed July 11, 2019, which is incorporated by reference in its entirety.

[0002] The present invention relates to systems and methods for the parallel implementation of multi-qubit quantum gates. [Background technology]

[0003] background Any unitary operation can be implemented on a quantum computer with a complete set of universal gates. The complete set of gates can consist of two-qubit controllable-NOT (CNOT) gates along with single-qubit operations. CNOT gates have been demonstrated in several different physical systems, such as trapped neutral atoms, trapped ions, superconducting circuits, and linear optics.

[0004] Quantum information processing with neutral atoms offers many interesting opportunities. Neutral atoms can be trapped in large numbers in flexible geometric structures using optical trapping techniques. Each individual atom can store a qubit of information in two hyperfine ground state levels |0> and |1>. Such storage has the advantages of high coherence times enabled by excellent isolation from the environment, near perfect qubit initialization via optical pumping, individual optical readout of each qubit, and direct manipulation of single qubits. Finally, strong and long-range interactions between atoms can be turned on by coupling to highly excited Rydberg states, enabling multi-qubit entanglement gates and universal quantum computing.

[0005] Protocols for entanglement of atoms using the Rydberg interaction have been explored theoretically and experimentally over the last decade, but despite significant advances, progress in this field has been limited by the relatively low fidelity associated with coherent control of the ground-Rydberg state.

[0006] As mentioned above, qubits encoded in the hyperfine states of neutral atoms can be entangled using controllability-phase (CZ) or CNOT gates mediated by Rydberg state interactions. A standard Rydberg-blockade CZ pulse sequence consists of a π pulse on the control qubit, a 2π pulse on the target qubit, and a π pulse on the control qubit, with 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 sits in the Rydberg level during the 2π pulse on the target qubit. The excitation and de-excitation of the target atom corresponds to a 2π rotation of effective spin 1 / 2, which therefore imparts a π phase shift to the wave function of the target atom. If the control atom blocks the target excitation, no rotation occurs and there is no phase shift of the target wave function. The result is a CZ controllability-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 computing gate set. Summary of the Invention [Problem to be solved by the invention]

[0007] However, single-qubit addressing of multi-qubit quantum gates remains experimentally challenging, as it requires the application of local π and 2π pulses to the control and target atoms, respectively.

[0008] Thus, there is a continuing need for improved systems and methods for the implementation of multi-qubit quantum gates. [Means for solving the problem]

[0009] overview In an exemplary embodiment, the present disclosure provides a method of operating a quantum gate on a grouping of qubits, the method comprising: selecting values ​​for a set of parameters of at least first and second laser pulses, where the parameters are selected from a relative phase shift, a laser frequency, a laser intensity and a pulse duration; and applying at least a first and a second laser pulse to all qubits in the group of N qubits, where N is equal to 2 or more, thereby coupling a non-interacting quantum state |1> to an interacting excited state |r>, such that each qubit that begins in quantum state |1> returns to state |1> upon completion of the at least the first and second laser pulses, and the qubits in the group are mutually blocked.

[0010] In another exemplary aspect, the present disclosure provides a method of operating a quantum gate on a collection of qubits, the method comprising: 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 a laser pulse to all qubits in the collection of N qubits, where N is equal to 3 or more, thereby coupling non-interacting quantum states |1> to interacting excited states |r>, such that each qubit that begins in quantum state |1> returns to state |1> upon completion of the laser pulse, and the qubits in the collection are mutually blocked.

[0011] In yet another exemplary embodiment, the present disclosure provides a device that includes a collection of N qubits, where N is equal to 2 or greater; and a coherent light source configured to apply at least first and second laser pulses to all qubits in the collection of N qubits, given selected values ​​for a set of parameters of at least first and second laser pulses, where the parameters are selected from relative phase shift, laser frequency, laser intensity, and pulse duration, to thereby couple a non-interacting quantum state |1> to an interacting excited state |r>, such that each qubit that begins in quantum state |1> returns to state |1> upon completion of the at least first and second laser pulses, and the qubits in the collection are mutually blocked.

[0012] In yet another exemplary embodiment, the present disclosure provides a device that includes a collection of N qubits, where N is equal to three or more; and a coherent light source configured to apply a laser pulse to all qubits in the collection of N qubits, given selected 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, thereby coupling a non-interacting quantum state |1> to an interacting excited state |r>, such that each qubit that begins in quantum state |1> reverts to state |1> upon completion of the laser pulse, and the qubits in the collection are mutually blocked.

[0013] The above system and method have many advantages, such as avoiding the need for rapid switching of lasers between different spatial locations, thereby enabling entanglement gate operation on large qubit arrays, and the simultaneous operation of multiple gates on multiple separate ensembles of atoms.

[0014] That is, the gist of the present invention relates to the following. Item 1 1. A method for operating a quantum gate on a collection of qubits, the method comprising: selecting values ​​for a set of parameters of at least the first and second laser pulses, the parameters being at least a relative phase shift between the first and second laser pulses, a laser frequency, a laser intensity, and a pulse duration; and applying at least a first and a second laser pulse, respectively, to all of the qubits in a gate, where the gate comprises a set of N qubits, N being equal to 2 or more, thereby coupling a non-interacting quantum state |1> to an interacting excited state |r>, such that each qubit that begins in quantum state |1> returns to state |1> upon completion of at least the first and second laser pulses, and all of the qubits in the set are mutually blocked; A method comprising: Section 2 the durations of at least the first and second laser pulses are selected such that if all of the qubits in the set begin in quantum state |1>, then all of the qubits in the set will return to quantum state |1> upon completion of each of the at least the first and second laser pulses; Optionally, the laser frequency of each pulse is detuned from the resonance transition between |1> and |r> by a detuning Δ, and the pulse duration t is

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[0015] The present invention may provide a system and method for the parallel implementation of multi-qubit quantum gates. [Brief description of the drawings]

[0016] BRIEF DESCRIPTION OF THE DRAWINGS Various objects, features, and advantages of the disclosed subject matter can be more fully understood by reference to the following detailed description of the disclosed subject matter when considered in conjunction with the following drawings, in which like reference numerals identify like elements and in which: [Figure 1A] FIG. 1A is a schematic showing the relevant atomic levels used in an exemplary embodiment of the system described herein. [Figure 1B] FIG. 1B is a schematic diagram showing atoms arranged in pairs used in an exemplary embodiment of the systems described herein. [Figure 1C] FIG. 1C is a plot of the |0> to |1> Rabi oscillations driven by a Raman laser used in an exemplary embodiment of the system described herein. [Figure 1D] FIG. 1D is a plot of the Rabi oscillations from |1> to |r> driven by a Rydberg laser used in an exemplary embodiment of the system described herein. [Figure 1E] FIG. 1E is a plot of the local phase shift for an addressed target atom and an unaddressed neighboring atom used in an exemplary embodiment of the system described herein. [Figure 2A] FIG. 2A is a schematic diagram showing a pulse sequence used in an exemplary embodiment of the system described herein. [Figure 2B] FIG. 2B is a schematic diagram showing the ground state used in an exemplary embodiment of the system described herein. [Figure 2C] FIG. 2C is a schematic diagram showing a two-level system used in an exemplary embodiment of the systems described herein. [Figure 2D] FIG. 2D is a Bloch sphere representation of a pulse sequence for the two-level system shown in FIG. 2C used in an exemplary embodiment of the system described herein. [Figure 2E] FIG. 2E is a plot of the accumulated phase shown in FIG. 2D as a function of detuning used in an exemplary embodiment of the system described herein. [Figure 2F] FIG. 2F is a schematic diagram showing another two-level system used in an exemplary embodiment of the systems described herein. [Figure 2G] FIG. 2G is a Bloch sphere representation of a pulse sequence for the two-level system shown in FIG. 2F used in an exemplary embodiment of the system described herein. [Figure 2H]FIG. 2H is a plot of the accumulated phase shown in FIG. 2G as a function of detuning used in an exemplary embodiment of the system described herein. [Figure 2I] FIG. 2I is a schematic showing the relevant atomic levels of a three-qubit gate used in an exemplary embodiment of the system described herein. [Figure 2J] FIG. 2J includes a Bloch sphere representation of a pulse sequence for the two-level system shown in FIG. 2I used in an exemplary embodiment of the system described herein. [Figure 2K] FIG. 2K includes a Bloch sphere representation of a pulse sequence for the two-level system shown in FIG. 2I used in an exemplary embodiment of the system described herein. [Figure 2L] FIG. 2L includes a Bloch sphere representation of a pulse sequence for the two-level system shown in FIG. 2I used in an exemplary embodiment of the system described herein. [Figure 2M] FIG. 2M includes a Bloch sphere representation of a pulse sequence for the two-level system shown in FIG. 2I used in an exemplary embodiment of the system described herein. [Figure 2N] FIG. 2N includes a Bloch sphere representation of a pulse sequence for the two-level system shown in FIG. 2I used in an exemplary embodiment of the system described herein. [Figure 2O] FIG. 2O includes a Bloch sphere representation of a pulse sequence for the two-level system shown in FIG. 2I used in an exemplary embodiment of the system described herein. [Figure 3A] FIG. 3A is a schematic diagram showing a quantum circuit used in an exemplary embodiment of the system described herein. [Figure 3B] FIG. 3B is a plot of the measured population of computational ground states used in an exemplary embodiment of the system described herein. [Figure 3C] FIG. 3C is a plot of parity oscillation as a function of accumulation phase used in an exemplary embodiment of the system described herein. [Figure 3D]FIG. 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] FIG. 3E is a plot of the probabilities of the four computational basis states used in an exemplary embodiment of the system described herein. [Figure 3F] FIG. 3F is a plot of a CNOT truth table used in an exemplary embodiment of the system described herein. [Figure 4A] FIG. 4A is a schematic diagram showing atoms arranged in triplets used in an exemplary embodiment of the system described herein. [Figure 4B] FIG. 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] FIG. 4C is a plot of the probabilities of the eight computational basis states used in an exemplary embodiment of the system described herein. [Figure 4D] FIG. 4D is a plot of a Toffoli truth table used in an exemplary embodiment of the system described herein. [Figure 5A] FIG. 5A is another schematic diagram showing the relevant atomic levels used in an exemplary embodiment of the system described herein. [Figure 5B] FIG. 5B is a schematic diagram showing Raman-assisted optical pumping used in an exemplary embodiment of the system described herein. [Figure 5C] FIG. 5C is a schematic diagram showing a quantum circuit used in an exemplary embodiment of the system described herein. [Figure 5D] FIG. 5D is a schematic diagram showing a quantum circuit used in an exemplary embodiment of the system described herein. [Figure 5E] FIG. 5E is a schematic diagram showing a quantum circuit used in an exemplary embodiment of the system described herein. [Figure 5F] FIG. 5F is a schematic diagram showing a quantum circuit used in an exemplary embodiment of the system described herein. [Figure 5G] FIG. 5G is a schematic diagram showing a quantum circuit used in an exemplary embodiment of the system described herein. [Figure 5H] FIG. 5H is a schematic diagram showing a quantum circuit used in an exemplary embodiment of the system described herein. [Figure 5I] FIG. 5I is a schematic diagram showing a quantum circuit used in an exemplary embodiment of the system described herein. [Figure 6] FIG. 6 is a plot of the time variation of the Rydberg-Rabi frequency and detuning used in an exemplary embodiment of the system described herein. [Figure 7A] FIG. 7A is a schematic diagram showing a quantum circuit for a controllable-phase gate used in an exemplary embodiment of the system described herein. [Figure 7B] FIG. 7B is a schematic diagram showing a pulse sequence used in an exemplary embodiment of the system described herein. [Figure 8A] FIG. 8A is a schematic diagram showing measurement statistics for the CNOT and Toffoli truth tables used in an exemplary embodiment of the system described herein. [Figure 8B] FIG. 8B is a schematic diagram showing measurement statistics for the CNOT and Toffoli truth tables used in an exemplary embodiment of the system described herein. [Figure 9] FIG. 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] FIG. 10 is a plot of the target probability for the Toffoli gate used in an exemplary embodiment of the system described herein. [Figure 11A] FIG. 11A is a schematic diagram showing another set of relevant atomic levels used in an exemplary embodiment of the system described herein. [Figure 11B] FIG. 11B is a schematic diagram showing atoms arranged in pairs in a continuous chain of atoms used in an exemplary embodiment of the systems described herein. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0017] Detailed Description As used herein, the term "qubit" can refer to either a theoretical unit of information in a quantum computer or a physical implementation of a unit of a quantum circuit. In either case, the term usually refers to a two-level quantum mechanical system with two basis states, denoted |0> and |1>. While a classical "bit", i.e., a theoretical unit of information in a conventional computer, can exist in either one of two states, denoted "0" or "1", a "qubit" can exist in any state that is a linear combination (superposition) of its two basis states. One example of a physical implementation of a quantum gate operated on two or more qubits includes an atom (or ion) that can be excited into a Rydberg state (i.e., a state with a very high value of the principal quantum number n).

[0018] According to some embodiments, the present disclosure describes methods and systems for operating quantum gates on a collection of N qubits, where N is equal to 2 or more qubits. The methods and systems described herein may be applied to a variety of qubits, such as atomic, ionic, and molecular qubits. In one exemplary embodiment, a method is introduced for realizing a multi-qubit entanglement gate between individual neutral atoms trapped in optical tweezers. The qubits are encoded into long-lasting hyperfine states |0> and |1> that can be individually or collectively coherently manipulated to perform single-qubit gates. The two-qubit gate, which is a controllability-phase gate, is performed using a protocol consisting of two global laser pulses driving neighboring atoms in a Rydberg blockade regime. As described further below, this gate achieves fidelity of 100%, ...

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[0019] According to one or more embodiments, each 87 Rb atoms are trapped in optical tweezers, sorted into groups of two or three 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 each individual qubit. As shown in Figures 1A-1B, the global driving field 110 in device 100 is generated by a 795 nm Raman laser, which, as described further below, is a 5S 1 / 2 From 5P 1 / 2The laser is tuned near the transition to . This laser is tuned in intensity to generate sidebands that drive the qubit via a two-photon Raman transition with an effective Rabi frequency Ω ≈ 2π × 250 kHz as shown in FIG. 1C. The local addressing beam 130 is generated by an acousto-optic deflector, which is 1 / 2 From 6P 3 / 2 A single 420 nm laser tuned near the transition to δ is split into several beams focused on individual atoms 131, resulting in an optical shift δ that is used for individual addressing. Coupling these two 5 S1 / 2 From 5P 1 / 2 and 5S 1 / 2 From 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 pushing atoms at |1> out of the trap with a resonant laser pulse, followed by site-resolved fluorescence imaging of the remaining atoms.

[0020] The multi-qubit gate uses a bichromatic Rydberg laser 120 containing light at 420 nm and 1013 nm to shift atoms from the qubit state |1> to the Rydberg state |r> = |70S 1 / 2 , m J= -1 / 2>. All atoms are uniformly coupled from the non-interacting quantum state |1> to the interacting excited state |r> via a two-photon process with a detuning Δ shown in FIG. 1D and an effective Rabi frequency Ω≈2π × 3.5 MHz. Within a given cluster of atoms 131 and 132, the Rydberg interaction between nearest neighbors 131 and 132 is 2π × 24 MHz ≫ Ω; thus, the neighboring atoms 131 and 132 proceed according to Rydberg blockade, such that the qubits 131 and 132 in the ensemble are mutually blocked in that they cannot be simultaneously excited to a Rydberg state. The protocols described herein can be applied to other mutually blocked qubits, such as mutually dipole blocked qubits. As shown in FIG. 1E, the local phase shift measured in the Ramsey sequence averaged over the five atom pairs 131 and 132 shown in FIG. 1B shows high contrast oscillations 135 for the addressed target atom 131 and limited (<2%) crosstalk 140 for the nearby unaddressed atom 132.

[0021] To entangle the atoms in such an array, a protocol is introduced herein for a two-qubit controllable-phase (CZ) gate that relies only on the global excitation of the atoms in the Rydberg blockade regime. As shown in FIG. 2B, the desired unitary CZ gate maps the computational ground states as follows: |00> → |00>, |01> → |01>e iφ , |10> → |10>e iφ , |11> → |11>e i(2φ-π) (1).

[0022] This map gives the canonical form of the controllability-phase gate up to the single qubit phase φ.

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[0023] The gate can be understood by considering the behavior of the four computational ground states. The |00> state is uncoupled by the laser field and therefore does not evolve. The dynamics of |01> (and |10>) are similar to that of a single atom.

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[0024] The parallel operation of the CZ gates can be shown on five separate pairs of atoms using the CZ gates and formalized using the quantum circuit shown in Figure 3A.

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[0025] The experimentally generated state ρ is the target Bell state

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[0026] The measured Bell state fidelity includes errors in state preparation and measurement (SPAM) as well as errors in the two-qubit entanglement gate. To specifically characterize the entanglement gate, as described further below, we assessed the error contribution from SPAM (1.2(1)%) per atom and estimated the SPAM correction fidelity.

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[0027] Further, the control of multiple atomic qubits is extended to implement a three-qubit controlled-controlled-phase (CCZ) gate. This logical operation can be decomposed into five two-qubit gates. Instead, this multiple control gate is realized by directly preparing the three atoms in a nearest-neighbor blockade configuration, with both outer atoms constraining the behavior of the middle atom. The complicated three-atom dynamics makes it difficult to analytically construct an overall laser pulse that implements a CCZ gate in this configuration. Therefore, numerical optimization is used to construct an overall amplitude- and frequency-modulated laser pulse that approximately implements the CCZ gate, as described further below. The laser pulse is optimized via a remote dressed chopped random basis (RedCRAB) optimal control algorithm.

[0028] As shown in FIG. 4A, the CCZ gate is implemented in parallel on four triplet 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 such that the nearest neighbors (410, 420 and 420, 430) are blocked by a strong 2π × 24 MHz interaction, similar to the two-qubit implementation. The edge atoms 410 and 430 interact weakly with each other (2π × 0.4 MHz). As with the two-qubit gate, the CCZ gate is embedded in a spin echo sequence to offset the optical shift, and the gate implements CCZ with a global X (π) rotation. The performance of this three-qubit gate is characterized by applying a local Hadamard to the middle atom 420 before and after the CCZ gate (to simplify implementation with the edge X (π) pulse, as shown in FIG. 4B and described further below) to convert it to a Toffoli gate. Eight computational basis states are prepared with an average fidelity of 95.3(3)%, as shown in FIG. 4C. A Toffoli gate is applied to each computational basis state to obtain truth table fidelity corrected for SPAM errors, as shown in FIG. 4D and described further below.

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[0029] These results can be straightforwardly improved and extended along several directions. The fidelity of Rydberg coupling is limited primarily by finite atomic temperatures and off-resonant laser scattering, which can be addressed by sideband cooling of the atoms in the optical tweezers and higher power lasers. Background atom 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 stronger constraints on the atomic ensemble.

[0030] Although we have demonstrated parallel gate execution on clusters of spatially separated atoms here, the same approach can be extended to nonlocal coupling in continuous atomic arrays using local addressing with additional off-resonance laser systems. Specifically, a subset of the array can be simultaneously illuminated to generate a light shift that brings them into resonance with a globally resonant Rydberg pumping laser, as described further below. Furthermore, as described further below, more atoms can be placed in the blockade volume and the controllable phase gates shown here 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 connectivity between qubits. The combination of the present results using recently demonstrated trapping and rearrangement of individual neutral atoms in two-dimensional (2D) and three-dimensional (3D) arrays is well suited to perform deep quantum circuits or fluctuating quantum optimization with hundreds of qubits. Such a platform could also be used to explore efficient methods for error correction and fault-tolerant operation, ultimately enabling scalable quantum processing.

[0031] Raman Laser The transitions between qubit states were driven using a 795 nm Raman laser, which was red-detuned at 2π × 100 GHz. 1 / 2 From 5P 1 / 2 The laser is coupled to a fiber-based Mach-Zehnder intensity modulator (Jenoptik AM785) that is DC biased around the transmission minimum. The modulator is driven at half the qubit frequency (ω 01 = 2π × 6.83 GHz), yielding sidebands at ±2π × 3.42 GHz, while the carrier and higher order sidebands are strongly suppressed. This approach is passively stable on timescales of days without any active feedback, in contrast to other approaches which generate sidebands via phase modulation and then isolate the suppression of the carrier mode using free-space engineered cavities or interferometers.

[0032] The Raman laser is aligned along the array of atoms (co-aligned with the 8.5 G bias field) and σ + Once deflected, the two sidebands coherently drive a π-transition between the F = 1 and F = 2 ground state manifolds with a Rabi frequency of Ω = 2π × 250 kHz, as shown in Figure 5 A. The Raman drive light induces a differential optical shift of 2π × 20 kHz on the qubit transition, and the drive frequency of the intensity modulator is adjusted to correct this optical shift when the Raman pulse is applied.

[0033] Optical pumping to |0> The atoms were pumped using a Raman-assisted pumping scheme with an 8.5 G magnetic field, |0>=|5S 1 / 2 , F=1, m F = 0>. As shown in Figure 5B, |5S 1 / 2 , F=1>For all m in the manifold F Coarse pumping of atoms into the |5S state 1 / 2 , F=2>~|5P 3 / 2, F=2> transition. Then, by detuning, we shift the population to |F=1, m F =-1> to |F=2, m F = -1>. The second pulse drives the population to |F=1, m F = +1> to |F=2, m F = +1>. The process is then repeated by again roughly pumping any ensemble that was moved to F = 2 back to the F = 1 manifold. The net effect of one cycle is |F=1, m F = ±1> a part of the population in |F=1, m F =0>. This cycle is typically repeated 70 times over a duration of 300 μs to achieve a |0> preparation fidelity of 99.3(1)%.

[0034] Rydberg laser system The atoms were then imaged via a two-color laser system at 420 nm and 1013 nm, with |1>=|5S 1 / 2 , F=2, m F =0> to |r>=|70S 1 / 2 , m J = -1 / 2>. The laser is coupled into the intermediate state |6P 3 / 2 > through σ - and σ + The transitions are biased to drive each of the |5S 1 / 2 , F=2, m F In the previous run using = -2>, the selection rule was |6P 3 / 2 It was ensured that only a single intermediate sublevel in and a single Rydberg state in could be coupled. Furthermore, the combined two-photon transition was magnetically insensitive.

[0035] |1>=|5S 1 / 2 , F=2, m FThe coupling from |70S =0> to the Rydberg state adds a little complexity, as described here. First, multiple intermediate states are coupled, and both |70S 1 / 2 , m J = ±1 / 2> sublevels can be reached. This is J = ±1 / 2 Rydberg levels spectrally, it is necessary to operate at a higher magnetic field. In the embodiment described herein, a magnetic field of 8.5 G corresponds to a m of 2π × 23.8 MHz. J = ±1 / 2. The matrix element is also reduced in coupling from |1> to |r>, while the laser scattering rate remains the same, and the transition now becomes magnetically sensitive. Nevertheless, this scheme can be easily coupled to Raman laser systems and benefits from high quality qubit states |0> and |1> in the ground state manifold that preserves coherence in optical tweezers. Note that the sensitivity to the electric field does not change with this scheme, but drifting or varying the electric field can be constrained such that the Rydberg resonance changes by less than 50 kHz.

[0036] One further complication in this implementation is the presence of another Rydberg state

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[0037] Building quantum circuits from native single-qubit gates All the above pulse sequences are decomposed into pre-calibrated single-qubit gates (and global multi-qubit gates, as shown above). The two single-qubit gates are X(π / 4), which is performed globally on all qubits simultaneously, and Z(π), which is performed by shifting the light from a laser focused on a single atom. In practice, the local Z(π) gates are applied to one atom from each cluster at a time (i.e. the atom to the left of each cluster or the atom in the middle of each cluster).

[0038] Computational ground state initialization For two qubits, all four computational basis states are initialized using a global X(π / 2) pulse (consisting of two successive X(π / 4) gates) and a local Z(π) gate for the left atom only (the top qubit in each circuit). The |00> state requires no pulses to be prepared, and the |11> state requires only a global X(π) gate. State |01> is prepared as shown in FIG. 5C, and state |10> is prepared as shown in FIG. 5D.

[0039] For three qubits, the eight computational basis states are reinitialized using an X(π / 2) pulse and a local Z(π) pulse that can be applied to any of the three atoms. |000> and |111> can each be reprepared with either no manipulation 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. First, |100> is prepared as shown in FIG. 5E. Second, preparation of |110> instead requires local addressing to the rightmost atom as shown in FIG. 5F.

[0040] Local X(π / 2) for CNOT gates

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[0041] Local Hadamard for Toffoli implementation To convert a CCZ gate into a Toffoli gate, we apply a local rotation to the target (middle) qubit before and after the CCZ pulse. The simplest way to achieve this given native gate set is to apply a global X(π / 4), then a local Z(π) and then a global X(3π / 4) to the middle qubit, as shown in Figure 5H.

[0042] For each end qubit, the net effect is simply an X(π) gate. For the intermediate qubits, the sequence continues with Hadamard gates (defined along a different axis than the typical definition), where

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[0043] Design of a two-qubit CZ gate This section provides a detailed theoretical discussion of the two-qubit gates realized herein. The desired unitary operations map the computational basis states as follows: |00> → |00>, |01> → |01> |10> → |10> |11> → |11>e iπ (3).

[0044] Up to global gauge selection (i.e. global rotation of qubits), this is equivalent to the following gate:

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[0045] To realize such a gate, both atoms are driven globally and uniformly with 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 pair of atoms is given by

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[0046] The dynamics of the system is decoupled into several simple sectors: (i) State |00> does not progress. (ii) If one of the atoms is in |0>, then only the other system evolves. The dynamics is therefore confined to the states |1> = |a1> and |r> = |b1> and the Hamiltonian

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[0047] A controlled phase gate can be constructed from two identical pulses of a Rydberg laser field of equal duration τ and detuning Δ with a phase jump (i.e., relative phase shift) by ξ between them. Each pulse changes the state of the atom according to the unitary U = exp(-iHτ). The change in the laser phase between the pulses, Ω → Ωe iξ effectively corresponds to driving the system about different axes on the Bloch sphere.

[0048] Describe the effect of both laser pulses combined

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[0049] Next, we consider the evolution of state |11>, where all qubits in the ensemble start out in quantum state |1>. Arbitrarily, the length or duration τ of each pulse is chosen such that the system prepared in state |11> experiences a complete detuned Rabi oscillation and returns to state |11> already after the first laser pulse; i.e.

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[0050] Finally, we consider the evolution of states |01> and |10>. In each case, this evolution 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 choice of Ω, Δ and τ. By a proper choice of the phase jump (i.e. the relative phase shift) between the first and second laser pulses ξ, it can always be ensured that the system returns to the state |10> (|01>) after the second laser pulse. The phase jump can be written as:

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[0051] Note that this construction can be generalized to multi-qubit controllable phase gates in fully blocked systems involving more than two atoms, as described further below.

[0052] Accounting for incomplete blockade The above analysis is based on the full blockade mechanism. Finite blockade interactions (and other imperfections such as couplings to other Rydberg states) can be accounted for, resulting only in an effective renormalization 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 restricted to the two states |a2> = |11> and |b2> = (|1r> + |r1>), a third state |c2> = |rr> needs to be considered, and H2 becomes

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[0053] 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 calculations relative to an experimentally calibrated Rydberg resonance. Both the pulse time and the phase jump between the pulses require experimental calibration due to perturbations in timing and phase associated with a control system based on an acousto-optic modulator (AOM). The pulse time τ is first calibrated by preparing both atoms in the qubit pair at |1> and driving them into the Rydberg state with the detuning Δ. Symmetrically excited states

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[0054] After fixing τ, only a single isolated atom is prepared at |1〉 and two pulses of length τ are driven with varying 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.

[0055] Finally, we can write the CZ gate (with single-particle phase φ) in the canonical form:

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[0056] This phase correction is performed by applying the entire 420 nm laser for a fixed time in the absence of the 1013 nm Rydberg light, which avoids any resonant Rydberg excitation and instead only adds a phase shift. To calibrate the phase correction, a Bell state sequence is applied, where the Bell state |Φ +>, and then a further X(π / 2) rotation is applied to both qubits. When the phase correction is optimal, the state |Ψ that can be measured in the ensemble is + > should be prepared. The global phase correction is done at the end of this sequence by |Ψ + >The measurement is modified to maximize the measured population.

[0057]

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[0058] Execution of CCZ gate The two-qubit gate above is

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[0059] The dynamics of the three atoms involved is given by the Hamiltonian

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[0060] An arrangement of three atoms such that all three atoms are within the blockade radius, i.e., all qubits in the ensemble are mutually blocked, so that no two atoms can be effectively excited to the Rydberg state simultaneously, V i,j We consider what it means that ≫ |Ω| ≫ |Δ|. Then, the only difference from the above discussion of the two-qubit controllable phase gate is that here there is an additional two-level system that needs to be considered, with the state |111〉 = |e〉,

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[0061] Using a sequence of pulses interspersed with jumps in the laser drive phase (i.e., relative phase changes),

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[0062] This pulse sequence is a generalization of the two-qubit pulse sequence described above, with p cycles (of equal length, Rabi frequency and detuning) and p-1 relative changes in the laser phase (ξ without loss of generality). p = 0). The controllable-controllable phase gate can be realized with p = 6 pulses and palindromic (e.g., symmetric) sequences of pulses, where ξ l = ξ p-l It is.

[0063] As used herein, the term "palindromic" when referring to an ordered sequence of pulses means that the sequence remains the same if the order is reversed. An example of a palindromic sequence of laser pulses is a "symmetric" sequence, i.e., a sequence of laser pulses starting at time t = t0 and ending at time t = t1, characterized in that a plot of the amplitude of the laser light as a function of time A = A(t) has reflection symmetry around the line t = 1 / 2(t1 - t0).

[0064] The pulse length or duration is again arbitrary.

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[0065] Three two-level systems, denoted A, B and C, are shown in FIG. 2I. The first pulses are denoted A10, B10 and C10 in FIGS. 2J-O. In FIGS. 2J-O, the notation X## is used, where the letter indicates the two-level system A, B or C, the first number indicates the pulse number 1-6 and the second number indicates the phase shift number 1-5. The first pulse C10, as shown on the Bloch sphere C10, is shown in system C of FIG. 2I.

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[0066] Another version of this gate is V 1,2 , V 2,3 ≫ |Ω|, |Δ| and V 1,3 It can be constructed when atoms are arranged such that |Ω|, |Δ|. Using the same palindrome (e.g., symmetric) 6-pulse ansatz described by equation (19), where the pulse length or duration τ is optionally

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[0067] As mentioned above, this controlled-controlled phase (CCZ) gate is bounded by the Rydberg blockade by the nearest neighbor, but the next nearest neighbor is V 1,2 , V 2,3 ≫ |Ω|, |Δ| and V 1,3 ≪ |Ω|, |Δ|. With this in mind, the CCZ gate implemented is guided by the fact that the atoms at both ends can simultaneously blockade the middle (target) atom. In particular, the following scheme can be considered to implement CCZ involving local excitation to a Rydberg state:

[0068] 1. Apply a π pulse to the atoms at both ends to move all of their populations in |1> to |r>. 2. A 2π pulse is applied to the central atom, exciting it from |1> to |r> and back to |1>, accumulating a π phase shift only if neither end atom is blocking the central atom and it is in |1>. 3. Apply another π-pulse to the edge atoms to shift any ensemble back from |r> to |1>. Such a protocol is the following unitary:

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[0069] In the absence of local excitations to Rydberg states, the global Rydberg coupling can still approximately realize this unitary. Because different input configurations evolve due to the dynamics of a few-level system with different coupling frequencies, it is difficult to design a single analytical global pulse to adequately control all input configurations. For example, the |001> state couples to |00r> as a two-level system with Rabi frequency Ω. The |011> state couples to |00r> as a two-level system with Rabi frequency Ω.

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[0070] 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 profile 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 the desired numerically simulated gate fidelity of 97.6%.

[0071] Further implementations with cooler atoms could achieve higher gate fidelity by designing the gate timing to intentionally offset the effects of unwanted phase accumulation between next-nearest neighbors. Alternatively, some qubit gates could be implemented with all atoms in the fully blocked regime by bringing the atoms closer together or by exciting them to a higher Rydberg state.

[0072] Spin-echo procedures for CZ and CCZ. The implementation of the controlled phase gate within the boxed region shown in FIG. 7A is shown in more clear detail to the right hand side of the equal sign.

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[0073] State readout via atomic loss The main technique used here for state readout is to apply a resonant laser pulse that heats the |1> (more generally F = 2) atoms outside the tweezers, and then take a fluorescence image of the remaining |0> atoms. This method accurately identifies the |0> atoms, but may miss atoms that have disappeared through background loss processes or due to residual Rydberg excitation on the |1> atoms, resulting in an overestimation of the |1> population. For any measurement involving Rydberg excitation, measurement statistics are collected both with and without a pushout pulse to provide an upper bound on how much leakage has occurred from the qubit subspace, and therefore also a lower bound on the true population of |1>.

[0074] This procedure is illustrated for a two-qubit experiment, with two types of measurements shown as A (|1> atom push is applied) and B (push is disabled). For each measurement procedure, statistics were obtained by observing four two-qubit states consisting of "disappearance" or "presence" for each qubit. The A vector relates these as |0> and |1>, so that A ij (

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[0075] A ij and B. ij Both of these are expressed as the basis set p αβ where

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[0076] A ij and B. ij When measuring, the target atomic group: p 00 , p 01 , p 10 and p 11 can be solved for

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[0077] All probabilities are non-negative,

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[0078] This is an analysis performed for the Bell state ensemble, the CNOT truth table, and the Toffoli truth table (extended to 3 qubits). For the truth tables, the analysis is performed for each measurement configuration (corresponding to different input computational basis states) shown separately as columns of the matrices in Figures 8A-B, showing the probability distributions (shown in terms of percentages) of the different output configurations both with and without the push pulse, as above.

[0079] Correction of state adjustment and measurement errors The problem of correcting the measured fidelity for state preparation and measurement (SPAM) errors is considered below. Let P be denoted as the probability to correctly initialize and measure all qubits; in general,

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[0080] Experimentally, the SPAM error is

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[0081] Bell State Fidelity The total probability that no error occurs for either of the two qubits is P = 97.6(2)%. Equation (47) keeps both ensemble and parity oscillation measurements separate. The ensemble measurements explicitly count only a lower bound on the ensemble of atoms in the qubit subspace (see section State readout via atom disappearance above). Therefore, there is no spurious contribution to the measured fidelity if an atom disappears. However, the measured fidelity does not distinguish between atoms pumped into magnetic sublevels outside the qubit subspace. If one of the two atoms is prepared in the incorrect magnetic sublevel (1.4(2)% probability),

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[0082] On the other hand, the parity oscillation amplitude does not suffer from spurious contributions from atoms being prepared or missing at the wrong sublevel, because this error is independent of the accumulated phase and therefore does not oscillate as a function of phase accumulation time. Therefore, the spurious contribution is

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[0083] CNOT truth table The truth table is measured by implementing the CNOT gate for each computational basis state. The basis states are prepared with finite fidelity, as measured and shown in FIG. 3E. For each basis state, it is desirable to evaluate how the finite output fidelity in the target state compares with the finite initialization fidelity to determine how well the gate implements this input state. The probability P of no SPAM errors occurring for each measurement setup is ij is established (where ij denotes the setting at which the computational basis state |ij> is initialized). Furthermore, the output establishment

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[0084] We now consider spurious contributions to the measured fidelity. If an error involving atom loss occurs, there is no spurious contribution to the fidelity since the fidelity measures only the atomic population within the qubit subspace. Alternatively, if an incorrect computational ground state is prepared,

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[0085] Toffoli Truth Table We perform the same analysis 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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[0086] Limited tomography of the Toffoli gate. The truth table of the Toffoli gate provides an indication of the magnitude of the gate's matrix elements expressed in a logical basis. However, the measured population does not carry information about the relative phase between the different entries. Implementing a similar procedure to the truth table, but rotating the Toffoli gate to operate on the X basis instead of the Z basis, allows some information about these phases to be recovered. A limited version of such a procedure has been used previously as a method to characterize the fidelity of the Toffoli gate, and is called "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 an X(±π / 2) rotation to all qubits before and after the Toffoli gate. The sign is chosen to be X(+π / 2) if the target qubit is initialized in |0>, and X(-π / 2) if the target qubit is initialized in |1>. Conditioning the sign of the rotation on the state of the target qubit ensures that the target qubit is always in the same state |+> before the operation of the Toffoli gate itself. y Force it to be in.

[0087] The Toffoli gate implemented herein, including the spin echo pulse (shown in FIG. 4B) acting as a global X(π) gate, is the unitary matrix:

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[0088] Performing the bounded tomography procedure on this unitary results in the following output truth table:

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[0089] It is noteworthy that the bounded tomography protocol only uses four of the eight X basis input states, as seen by the fact that the target qubit is always initialized to |+>. This makes four of the eight measurements equivalent to the other four up to a total X (π) rotation at the end. Comparing these two sets of measurements provides a bound on the probability of leakage from the qubit subspace, similar to the approach described above in section "State readout via atomic annihilation".

[0090] Concurrent gate execution in continuous arrays. The above embodiment involves the execution of parallel multi-qubit gates on separate pairs of atoms, where the interaction between the pairs is negligible. However, this protocol can be extended to parallel gate execution on a serial chain 1100 of atoms, as illustrated in Figures 11A and 11B. Consider an additional local addressing laser system 1130 that can address any subset of atoms, for example using an acousto-optic deflector. Specifically, the wavelength can be chosen for this laser such that the imparted 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 additional local addressing laser 1130 does not apply any qubit manipulation, but instead simply shifts the effective Rydberg resonance by δ. Near-infrared wavelengths tuned away from any ground-state optical transition

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[0091] With such a system one can illuminate all pairs of adjacent atoms 1131 and 1132 for which one intends to perform a two-qubit gate, and then perform a multi-qubit gate in parallel on all pairs by tuning the Rydberg laser to a light-shifted resonance. The only constraint is that there must be sufficient space between the addressed pairs 1131 and 1132 so that the interaction (crosstalk) between them is negligible at a particular layer of gate implementation.

[0092] Multiqubit gates for a fully blocked ensemble of N qubits. Consider an ensemble or collection of N fully blocked qubits (N=K), where at most one qubit can be excited into the Rydberg state |r> simultaneously. In addition to the interacting Rydberg state |r>, the atomic qubit has two non-interacting qubit states |0> and |1>. Under laser-driven operation, which couples state |1> to state |r> with the Rabi frequency Ω and detuning Δ, the atomic ensemble evolves as an effective two-level system with an "enhanced" Rabi frequency, depending on how many atoms start out in the qubit state |1> (rather than |0>). There are N+1 such possible configurations, with the number of atoms starting out in |1> (denoted M) ranging from 0 to N. Each such system has an enhanced Rabi frequency

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[0093] The most general N-qubit gate that can be implemented by the overall laser pulse protocol described here is φ M Each of these N+1 configurations (labeled |M>, from 0 to N for M) returns to their initial state with a phase accumulation of |M>. More specifically, if U is a unitary describing the operation of the gate, then each initial configuration |M> can be written as

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[0094] When designing a gate, the specific topology is:

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[0095] A laser pulse sequence Ansatz is defined to implement any target gate specified by the 2N-1 constraint. The sequence consists of 4N-6 laser pulses with respective detunings Δ and duration τ, with the laser phase shift between each pulse being the relative phase shift

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[0096] Optionally, the pulse duration τ is chosen such that one of the configurations |M> returns to its initial state after each laser pulse. This is

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[0097] Gate Phase

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[0098] As discussed above, for N = 2, Δ / Ω = 0.377371, ξ1 = 3.90242. For N = 3, multiple solutions are found, and four sample solutions are shown in Table 3. Note that solution 3 is the same solution discussed above where ξ2 + 2π and ξ3 + 2π. [Table 3]

[0099] For N = 4, multiple solutions were found, and four sample solutions are shown in Table 4. [Table 4]

[0100] For N = 5, multiple solutions were found and two sample solutions are shown in Table 5. [Table 5]

[0101] Type C N-1 Z(π) gate (

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[0102] Since a CZ(π) gate on a single pair can be understood as adding a π phase shift to the basis state where both qubits in the pair start at |1〉, the action of CZ(π) on all pairs in the system can be understood as adding a π phase shift to all pairings of qubits in a basis state that is |1〉. For a basis state |M〉, which is a superposition of all combinations of M qubits starting at |1〉, the number of qubits that undergo a π phase shift is exactly

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[0103] Overall pulse with time-dependent intensity and detuning profile The most general pulses that can be described are laser pulses with total duration T, a time-dependent intensity profile I(t) and a time-dependent detuning profile Δ(t), each defined for 0≦t≦T, so that arbitrarily, the time-dependent values ​​of the laser intensity, the laser frequency, the laser phase and the pulse duration are selected based on the conditional phase angle θ. In principle these profiles can be any function of time, but practical experimental limits set upper and lower bounds on the values ​​of the functions. For example, there are practical limits on the maximum value of I(t) (how much laser power is available) and on the range of Δ(t) (how far the laser can be smoothly detuned). Experimental limits also set bounds on the continuity and smoothness of the frequency spectrum of these functions or equivalently these profiles. Some limits on the high frequency components mentioned above (depending on the implementation choice) are not possible to realize experimentally.

[0104] How do we find to implement a target gate within this bounded (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)), and 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, one can identify what is the ideal output state of the target gate. For example, a target gate can be modeled using the unitary operator U ゲート In this case, the target output state can be expressed as |ψ 標的 >= U ゲート The actual gate implemented by the laser pulse with I(t) and Δ(t) is the numerically simulated output state |ψ sim A figure of merit can be defined that characterizes how close the simulated output state is to the target output state: fidelity

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[0105] Thus, in a first exemplary embodiment, the invention is a method of operating a quantum gate on a collection of qubits. In a first aspect of the first exemplary embodiment, the method includes the steps of selecting values ​​for a set of parameters of at least a first and a second laser pulse, where the parameters are selected from a relative phase shift, a laser frequency, a laser intensity, and a pulse duration; and applying at least a first and a second laser pulse to all qubits in a collection of N qubits, where N is equal to 2 or more, thereby coupling a non-interacting quantum state |1> to an interacting excited state |r>, such that each qubit that starts in a quantum state |1> returns to a state |1> upon completion of at least the first and the second laser pulse, and the qubits in the collection are mutually blocked, e.g., dipole blocked or Rydberg blocked.

[0106] In a second aspect of the first exemplary embodiment, each qubit may be an atomic qubit, an ionic qubit, or a molecular qubit.

[0107] In a third aspect of the first exemplary embodiment, all qubits in the set are mutually blocked. Other features and exemplary features of the method are as described above with respect to the first to second aspects of the first exemplary embodiment.

[0108] In a fourth aspect of the first exemplary embodiment, the duration of at least the first and second pulses is selected such that if all qubits in the set start out in quantum state |1>, then upon completion of each of the at least the first and second laser pulses, all qubits in the set return to quantum state |1>. For example, the laser frequency of each pulse is detuned from the resonant transition between |1> to |r> by a detuning Δ, and the pulse duration t is

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[0109] In a 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 as described above with respect to the first through fourth aspects of the first exemplary embodiment.

[0110] In a 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 as described above with respect to the first through fifth aspects of the first exemplary embodiment.

[0111] In a seventh aspect of the first exemplary embodiment, the gate is a controlled phase gate C N-1 Z(θ), where θ is the conditional phase angle. For example, N is 2. In another example, the quantum gate is a controlled 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 controlled phase gate. In yet a further example, the laser frequency is detuned from the resonant transition between |1> and |r> by a detuning Δ, 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 as described above with respect to the first to sixth aspects of the first exemplary embodiment.

[0112] In an eighth aspect of the first exemplary embodiment, N is 3. In the eighth aspect, the quantum gate is a controlled-controlled phase (C 2Z(θ) gate. For example, the laser frequency, pulse duration and phase shift of each of at least the first and second laser pulses are selected based on the conditional phase angle θ. Other features and exemplary features of the method are as described above with respect to the first to seventh aspects of the first exemplary embodiment.

[0113] In a ninth aspect of the first exemplary embodiment, N is 3 and the method includes applying a sequence of six pulses. The sequence of six pulses may be a palindrome. Other features and exemplary features of the method are as described above with respect to the first through eighth aspects of the first exemplary embodiment.

[0114] In a tenth aspect of the first exemplary embodiment, the method includes applying a sequence of 4N-6 pulses. For example, the sequence of pulses can be a palindrome. Other features and exemplary features of the method are as described above with respect to the first to ninth aspects of the first exemplary embodiment.

[0115] In a second exemplary embodiment, the invention is a method of operating a quantum gate on a collection of qubits. In a 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 a laser pulse to all qubits in a collection of N qubits, where N is equal to 3 or more, thereby coupling non-interacting quantum states |1> to interacting excited states |r>, such that each qubit that starts in quantum state |1> returns to state |1> upon completion of the laser pulse, and the qubits in the collection are mutually blocked, e.g., dipole blocked or Rydberg blocked.

[0116] In a second aspect of the second exemplary embodiment, each qubit can be an atomic qubit, an ionic qubit, or a molecular qubit.

[0117] In a third aspect of the second exemplary embodiment, all of the qubits in the set are mutually blocked. Other features and exemplary features of the method are as described above with respect to the first to second aspects of the second exemplary embodiment.

[0118] In a 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 as described above with respect to the first through third aspects of the second exemplary embodiment.

[0119] In a fifth aspect of the second exemplary embodiment, the gate is a controlled phase gate C N-1 Z(θ), where θ is the conditional phase angle. Other features and exemplary features of the method are as described above with respect to the first to fourth aspects of the second exemplary embodiment.

[0120] In a sixth aspect of the second exemplary embodiment, N is 3. Other features and exemplary features of the method are as described above with respect to the first to fifth aspects of the second exemplary embodiment.

[0121] In a seventh aspect of the second exemplary embodiment, N is 3 and the quantum gate is a controllable-controllable phase (C 2 Z(θ) gate. For example, the time-dependent values ​​of the laser intensity, laser frequency, laser phase and pulse duration are selected based on the conditional phase angle θ. In another example, the conditional phase angle θ=π. Other features and exemplary features of the method are as described above with respect to the first to sixth aspects of the second exemplary embodiment.

[0122] In a third exemplary embodiment, the invention is a device. In one aspect of the third exemplary embodiment, the device includes: a collection of N qubits, where N is equal to 2 or more; and a coherent light source configured to apply at least a first and a second laser pulse to all qubits in the collection of N qubits, thereby coupling a non-interacting quantum state |1> to an interacting excited state |r>, given selected values ​​for a set of parameters of at least a first and a second laser pulse, where the parameters are selected from a relative phase shift, a laser frequency, a laser intensity, and a pulse duration, such that each qubit that starts in a quantum state |1> returns to a state |1> upon completion of at least the first and the second laser pulse, and the qubits in the collection are mutually blocked.

[0123] Other features and exemplary features of the third exemplary embodiment are as described above with respect to various aspects of the first exemplary embodiment.

[0124] In a fourth exemplary embodiment, the invention is a device. In one aspect of the fourth exemplary embodiment, the device includes: a collection of N qubits, where N is equal to 3 or more; and a coherent light source configured to apply a laser pulse to all qubits in the collection of N qubits, thereby coupling non-interacting quantum states |1> to interacting excited states |r>, such that each qubit that starts in quantum state |1> reverts to state |1> upon completion of the laser pulse, and the qubits in the collection are mutually blocked.

[0125] Other features and exemplary features of the fourth exemplary embodiment are as described above with respect to various aspects of the second exemplary embodiment.

[0126] Although some exemplary aspects are thus described, it is understood that various variations, modifications, and improvements will be readily apparent to those skilled in the art. Such variations, modifications, and improvements are intended to form part of the present disclosure and are intended to be within the spirit and scope of the present disclosure. Although some examples shown herein include specific combinations of functions or structural elements, it should be understood that these functions and elements can be combined in other ways according to the present disclosure to achieve the same or different purposes. In particular, acts, elements, and features discussed with respect to one embodiment are not intended to be excluded from similar or other roles in other embodiments. Furthermore, the elements and components described herein may be further divided into additional components or combined together to form fewer components for performing the same functions. Accordingly, the foregoing description and accompanying drawings are intended to be illustrative only and not limiting.

[0127] The aspects of the present invention include the following. Item 1 1. A method for operating a quantum gate on a collection of qubits, the method comprising: selecting values ​​for a set of parameters of at least the first and second laser pulses, the parameters being selected from a relative phase shift, a laser frequency, a laser intensity, and a pulse duration; and applying at least a first and a second laser pulse to all qubits in a collection 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>, such that each qubit that begins in quantum state |1> returns to state |1> upon completion of at least the first and second laser pulses, and the qubits in the collection are mutually blocked; A method comprising: Section 2 Item 2. The method of item 1, wherein each qubit is an atomic qubit. Section 3 Item 2. The method of item 1, wherein each qubit is an ion qubit. Section 4 Item 2. The method of item 1, wherein each qubit is a molecular qubit. Section 5 5. The method of any one of paragraphs 1 to 4, wherein the mutually blocked qubits in the ensemble are dipole blocked to each other. Section 6 3. The method of claim 1 or 2, wherein the mutually blocked qubits in the ensemble are Rydberg blocked to each other. Section 7 7. The method of any one of paragraphs 1 to 6, wherein all qubits in the ensemble are mutually blocked. Section 8 8. The method of claim 7, wherein the durations of at least the first and second laser pulses are selected such that if all qubits in the set start out in quantum state |1>, then all qubits in the set return to quantum state |1> upon completion of each of the at least the first and second laser pulses. Section 9 The laser frequency of each pulse is detuned from the resonance transition between |1> and |r> by a detuning Δ, and the pulse duration t is

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Claims

1. 1. A method for operating a quantum gate on a collection of qubits, the method comprising: selecting values ​​for a set of parameters of at least the first and second laser pulses, the parameters being at least a relative phase shift between the first and second laser pulses, a laser frequency, a laser intensity, and a pulse duration; and applying at least a first and a second laser pulse, respectively, to all of the qubits in a gate, where the gate comprises a set of N qubits, N being equal to 2 or more, thereby coupling a non-interacting quantum state |1> to an interacting excited state |r>, such that each qubit that begins in quantum state |1> returns to state |1> upon completion of at least the first and second laser pulses, and all of the qubits in the set are mutually blocked; A method comprising:

2. the durations of at least the first and second laser pulses are selected such that if all of the qubits in the set begin in quantum state |1>, then all of the qubits in the set return to quantum state |1> upon completion of each of the at least the first and second laser pulses; Optionally, the laser frequency of each pulse is detuned from the resonance transition between |1> and |r> by a detuning Δ, and the pulse duration t is [0010] where Ω is the Rabi frequency of the laser pulse. The method of claim 1 , wherein the Δt is equal to:

3. 3. The method of claim 1 or 2, wherein 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.

4. The gate is a controlled phase gate C N-1 4. The method of claim 1, wherein Z(θ) is a conditional phase angle.

5. The method of any one of claims 1 to 4, wherein N is 2.

6. the quantum gate is a controlled phase (CZ(θ)) gate, N=2, and the laser frequency, pulse duration and phase shift are selected based on a conditional phase angle θ of the controlled phase gate; Optionally, the laser frequency is detuned from the resonance transition between |1> and |r> by a detuning Δ, and the laser intensity is selected such that the Rabi frequency of the laser pulse is Ω; 6. The method of claim 5, further optionally, wherein the laser frequency, laser intensity, pulse duration and phase shift are selected such that the conditional phase angle θ=π.

7. The method of any one of claims 1 to 4, wherein N is 3.

8. A quantum gate has a controllable-controllable phase (C 2 8. The method of claim 7, wherein the first and second laser pulses are each a conditional Z(θ) gate, N is 3, and a laser frequency, a pulse duration and a phase shift of each of the at least first and second laser pulses are selected based on a conditional phase angle θ.

9. The method includes applying a sequence of 4N-6 pulses; 4. The method of claim 1, 2 or 3, wherein optionally N is 3 and the method comprises applying a sequence of 6 pulses.

10. 1. A method for operating a quantum gate on a collection of qubits, the method comprising: selecting time-dependent values ​​for a set of parameters of the laser pulse, the parameters being laser phase, laser frequency, laser intensity and pulse duration; and applying a laser pulse to all qubits in a gate consisting of a set of N qubits, where N is equal to 3 or more, thereby coupling non-interacting quantum states |1> to interacting excited states |r>, such that each qubit that begins in quantum state |1> reverts to state |1> upon completion of the laser pulse and all qubits in the set are mutually blocked; A method comprising:

11. (a) time-dependent values ​​of laser intensity, laser frequency, pulse duration and laser phase are selected to achieve the desired fidelity of the quantum gate; (b) The gate is a controlled phase gate C N-1 Z(θ), where θ is the conditional phase angle; (c) N is 3; (d) N is 3 and the quantum gate has a controllable-controllable phase (C 2 Z(θ)) gate; (e) N is 3 and time-dependent values ​​of the laser intensity, laser frequency, laser phase and pulse duration are selected based on the conditional phase angle θ; (f) N is 3 and the conditional phase angle θ = π.

11. The method of claim 10, wherein the

12. The method of any one of claims 1 to 11, wherein each qubit is an atomic qubit, an ionic qubit or a molecular qubit.

13. (a) all qubits in the ensemble are mutually blocked, or 13. The method of claim 1, wherein (b) each qubit is an atomic qubit, and wherein mutually blocked qubits in the ensemble are Rydberg blocked to each other.

14. at least one gate consisting of a set of N qubits, where N is equal to or greater than 2; and Given selected values ​​for a set of parameters of at least the first and second laser pulses, where the parameters are at least a relative phase shift between the first and second laser pulses, a laser frequency, a laser intensity, and a pulse duration: a coherent light source configured to apply at least a first and a second laser pulse, respectively, to all of the qubits in the at least one gate, thereby coupling a non-interacting quantum state |1> to an interacting excited state |r>, such that each qubit that begins in quantum state |1> reverts to state |1> upon completion of the at least first and second laser pulses, and all of the qubits in the ensemble are mutually blocked. Including, the device.

15. at least one gate consisting of a set of N qubits, where N is equal to or greater than 3; and Given selected time-dependent values ​​for a set of parameters of a laser pulse, where the parameters are laser phase, laser frequency, laser intensity and pulse duration: a coherent light source configured to apply a laser pulse to all of the qubits in the at least one gate, thereby coupling a non-interacting quantum state |1> to an interacting excited state |r>, such that each qubit that begins in quantum state |1> reverts to state |1> upon completion of the laser pulse, and all of the qubits in the ensemble are mutually blocked. Including, the device.

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