EP4705885A2 - Codes de contrôle de parité à faible densité quantique avec réseaux d'atomes reconfigurables - Google Patents

Codes de contrôle de parité à faible densité quantique avec réseaux d'atomes reconfigurables

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Publication number
EP4705885A2
EP4705885A2 EP24914477.5A EP24914477A EP4705885A2 EP 4705885 A2 EP4705885 A2 EP 4705885A2 EP 24914477 A EP24914477 A EP 24914477A EP 4705885 A2 EP4705885 A2 EP 4705885A2
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European Patent Office
Prior art keywords
qubits
code
quantum
qubit
codes
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Pending
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EP24914477.5A
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German (de)
English (en)
Inventor
Hengyun Zhou
Juan Pablo BONILLA ATAIDES
Dolev BLUVSTEIN
Jonathan Wurtz
Mikhail D. Lukin
Qian Xu
Liang Jiang
Christopher A. PATTISON
Nithin RAVEENDRAN
Bane Vasic
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Quera Computing Inc
University of Chicago
California Institute of Technology
Harvard University
University of Arizona
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Quera Computing Inc
University of Chicago
California Institute of Technology
Harvard University
University of Arizona
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Publication of EP4705885A2 publication Critical patent/EP4705885A2/fr
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    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena
    • G06N10/70—Quantum error correction, detection or prevention, e.g. surface codes or magic state distillation
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena
    • G06N10/20—Models of quantum computing, e.g. quantum circuits or universal quantum computers
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena
    • G06N10/40—Physical realisations or architectures of quantum processors or components for manipulating qubits, e.g. qubit coupling or qubit control
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N5/00—Computing arrangements using knowledge-based models
    • G06N5/01—Dynamic search techniques; Heuristics; Dynamic trees; Branch-and-bound

Definitions

  • a plurality of data qubits is provided, each of the plurality of data qubits disposed in a corresponding trap.
  • a plurality of ancilla qubits is provided, each of the plurality of ancilla qubits disposed in a corresponding trap.
  • the plurality of data qubits and the plurality HQU-01325 HU 9348 of ancilla qubits are arranged in a plurality of rows and a plurality of columns, thereby forming a lattice.
  • a plurality of permutations of the plurality of rows and the plurality of columns is performed, each of the plurality of permutations placing each of the plurality of data qubits within an interaction radius of one of the plurality of ancilla qubits, thereby forming a plurality of proximate pairs.
  • a global control pulse is applied to the lattice, thereby applying a gate to each of the plurality of proximate pairs, and thereby encoding a parity check matrix between the plurality of ancilla qubits and the plurality of data qubits.
  • a control laser pulse is applied to the plurality of data qubits to thereby prepare them in an initial state.
  • arranging the plurality of data qubits and the plurality of ancilla qubits in the lattice comprises moving, in parallel, the plurality of ancilla qubits into the lattice.
  • performing the plurality of permutations comprises moving, in parallel, one or more rows within the lattice and moving, in parallel, one or more columns within the lattice.
  • the plurality of ancilla qubits comprises Z stabilizers and X stabilizers.
  • a subset of the plurality of ancilla qubits is removed from the lattice and a measurement is performed on the subset.
  • the subset corresponds to Z stabilizers. In other embodiments, the subset corresponds to X stabilizers.
  • performing the plurality of permutations comprises determining a collision-free path for each of the plurality of data qubits and each of the plurality of ancilla qubits for each of the plurality of permutations.
  • determining the collision-free path comprises bipartition and recursive sorting of the plurality HQU-01325 HU 9348 of data qubits and the plurality of ancilla qubits.
  • the collision-free path is a cubic spline.
  • determining the collision-free path comprises: decomposing the parity check matrix into a first product graph and a second product graph; determining a routing of the plurality of rows according to the first product graph; and determining a routing of the plurality of columns according to the second product graph.
  • the plurality of permutations comprises row-specific and/or column-specific permutations.
  • performing the plurality of permutations comprises: applying a pinning beam to at least one qubit of the plurality of data qubits or the plurality of ancilla qubits, thereby maintaining the position of the at least one qubit according to the routing of the plurality of rows or columns.
  • the parity check matrix implements a quantum low-density parity-check (qLDPC) code.
  • the parity check matrix implements a surface code.
  • the parity check matrix implements a hypergraph product (HGP) code.
  • the parity check matrix implements a Calderbank-Shor-Steane (CSS) code.
  • the parity check matrix implements a Lifted Product (LP) code.
  • the LP code prior to performing the plurality of permutations, is flattened.
  • flattening the LP code comprises iteratively dividing and flattening the LP code.
  • the gate applied to each of the plurality of proximate pairs is a CZ gate.
  • the global control pulse is a laser pulse.
  • the trap corresponding to each of the plurality of data qubits and to each of the plurality of ancilla qubits is an optical trap.
  • the HQU-01325 HU 9348 optical traps corresponding to the plurality of data qubits and to the plurality of ancilla qubits are generated by directing a beam of light to at least one acousto-optic deflector (AOD), and moving the one or more rows and moving the one or more columns comprises varying a drive frequency of the at least one AOD.
  • AOD acousto-optic deflector
  • one or more rotations is applied during said moving.
  • applying the one or more rotations comprises applying a Raman pulse.
  • a quantum computing system comprising a plurality of data qubits, each disposed in a corresponding trap, and a plurality of ancilla qubits, each disposed in a corresponding trap, wherein the quantum computing system is configured to perform any of the forgoing methods.
  • Fig.1 is a schematic view of a quantum information architecture according to embodiments of the present disclosure.
  • Fig.2 is a level diagram showing key 87 Rb atomic levels according to embodiments of the present disclosure.
  • Fig.3 is a schematic view of a quantum processing unit (QPU) according to embodiments of the present disclosure.
  • Fig.4 is a schematic view of a lattice of qubits illustrating the product structure of hypergraph product codes according to embodiments of the present disclosure.
  • Figs.5A-C are schematic views of lattices of qubits, illustrating column and row permutations according to embodiments of the present disclosure.
  • Fig.6 is a schematic view of a 1-dimensional array of qubits over time, showing a syndrome extraction gate sequence according to embodiments of the present disclosure.
  • Fig.7 is a schematic view of a 1-dimensional array of qubits over time, showing the steps of a rearrangement according to embodiments of the present disclosure.
  • Figs.8A-AA are schematic views of a 1-dimensional array of qubits forming a sequence of rearrangement steps to achieve permutation according to embodiments of the present disclosure.
  • Fig.9 is a schematic view of a 1-dimensional array of qubits over time, showing the steps of a rearrangement according to embodiments of the present disclosure.
  • Fig.10 is a schematic view of an exemplary 2-dimensional graph according to embodiments of the present disclosure.
  • Fig.11 is a schematic view of a 1-dimensional array of qubits over time, showing the use of pinning beams to prevent movement in some columns according to embodiments of the present disclosure.
  • Fig.12 is a schematic view of a lattice of qubits illustrating the product structure of lifted product (LP) codes according to embodiments of the present disclosure.
  • Fig.13 is pseudocode for an algorithm for arbitrary 1D atom rearrangement in a logarithmic number of steps according to embodiments of the present disclosure.
  • Fig.14 is pseudocode for a product coloration circuit for HGP syndrome extraction according to embodiments of the present disclosure.
  • Fig.15 is pseudocode for a pipelined product coloration circuit for multi-round HGP syndrome extraction according to embodiments of the present disclosure.
  • Figs.16A-D illustrate the efficient implementation of quantum LDPC codes with atom arrays according to embodiments of the present disclosure.
  • Figs.17A-B illustrate the ordering of operations in pipelined syndrome extraction according to embodiments of the present disclosure.
  • HQU-01325 HU 9348 Fig.18 is a schematic view of an apparatus for quantum computation according to embodiments of the present disclosure.
  • Quantum low-density parity-check (qLDPC) codes can achieve high encoding rates and high code distances, providing a promising route to low-overhead fault-tolerant quantum computing.
  • the high connectivity required to implement such codes makes their physical realizations challenging.
  • the present disclosure provides a scheme to efficiently implement constant-rate qLDPC codes with reconfigurable atom arrays. This scheme utilizes the product structure inherent in many qLDPC codes to provide streamlined circuit implementations of them.
  • a quantum bit is the fundamental building block for a quantum computer.
  • qubits can occupy two distinct states labeled
  • multiple qubits are entangled in order to build multi-qubit quantum gates.
  • Bits and qubits are each encoded in the state of real physical systems.
  • a classical bit (0 or 1) may be encoded in whether a capacitor is charged or discharged, or whether a switch is ‘on’ or ‘off’.
  • HQU-01325 HU 9348
  • the term qudit denotes the unit of quantum information that can be realized in suitable ⁇ -level quantum systems.
  • a collection of qubits that can be measured to ⁇ states can implement an ⁇ -level qudit.
  • Quantum bits are encoded in quantum systems with two (or more) distinct quantum states. There are many physical realizations that may be employed. One example is based on individual particles such as atoms, ions, or molecules which are isolated in vacuum.
  • a qubit may be encoded in any pair of quantum states of the atom/ion/molecule.
  • Coherence measures the lifetime of the qubit before its information is lost. It has a close analogy with classical bits: if you prepare a classical bit in the 0 state, then after some time it may randomly be flipped to 1 due to environmental noise. Quantum mechanically, the same error may occur:
  • qubits may suffer from additional errors: for example, a superposition state (
  • the qubits In real quantum computers, the qubits must be encoded in quantum states which have long coherence properties.
  • Quantum computers generally can contain many qubits, each encoded in its own atom/molecule/ion/etc. Beyond simply containing the qubits, the quantum computer should be able to (1) initialize the qubits, (2) manipulate the state of the qubits in a controlled way, and (3) read out the final states of the qubits.
  • one type of qubit manipulation is a so-called single-qubit gate, which means an operation that is applied individually to a qubit. This may, HQU-01325 HU 9348 for example, flip the state of the qubit from
  • the second necessary type of qubit manipulation is a multi-qubit gate, which acts collectively on two or more qubits, including those that are entangled. A multi- qubit gate is realized through some form of interaction between the qubits.
  • a qubit is encoded in two near- ground-state energy levels of an atom, ion, or molecule.
  • An example of this is a hyperfine qubit.
  • Such a qubit is encoded in two electronic ground states that differ by the relative orientation of the nuclear spin with respect to the outer electron spin. Pairs of such states can be chosen so that they are particularly robust / insensitive to environmental perturbations, leading to long coherence times.
  • the atom/ion/molecule can absorb a photon from one frequency component and coherently emit into a different frequency component, and in doing so it changes its state.
  • This approach benefits from the capability of focusing the laser field onto individual particles or subsets of particles in the quantum computer.
  • the laser field can also be applied with high intensity, enabling much faster gate operations.
  • Neutral atom quantum computers encode qubits in individual neutral atoms.
  • the neutral atoms are trapped in a vacuum chamber and levitated by trapping lasers.
  • the trapping lasers are individual optical tweezers, which are individual tightly focused laser beams that trap an individual atom at the focus.
  • a typical approach for encoding a qubit in neutral atoms is the hyperfine qubit approach, in which two ground states split by several GHz form the qubit.
  • Multi-qubit gates in neutral atom quantum computers are realized using a third atomic state, which is a highly- excited Rydberg state. When one atom is excited to a Rydberg state, neighboring atoms are prevented from being excited to the Rydberg state. This conditional behavior forms the basis for multi-qubit gates, such as a controlled-NOT gate.
  • the Rydberg state is used temporarily HQU-01325 HU 9348 to mediate the multi-qubit gate, and then the atoms are returned back from the Rydberg state to the ground state levels to preserve their coherence.
  • Trapped ion quantum computers use atomic species that are ionized, meaning they have a net charge. In most cases, many ions are trapped in one large trapping potential formed by electrodes in a vacuum chamber. The ions are pulled to the minimum of the trapping potential, but inter-ion Coulomb repulsion causes them to form a crystal structure centered in the middle of the trapping potential. Most commonly, the ions arrange into a linear chain.
  • Qubits are encoded in trapped ions in multiple ways.
  • One common approach is to use ground-state hyperfine levels, as described for neutral atoms.
  • single-qubit gates may use microwave radiation or stimulated Raman transitions.
  • trapped ion hyperfine qubits rely heavily on stimulated Raman transitions for performing multi-qubit gates.
  • Stimulated Raman transitions may be used to control both the hyperfine state of the ion but also to change the motional state of the ion (i.e., add momentum). This can be understood as absorbing a photon moving in one direction and emitting a photon in a different direction, such that the difference in photon momentum is absorbed by the ion. Since many ions are often trapped in one collective trapping potential and are mutually repelling one another, changing the motional state of one ion affects other ions in the system, and this mechanism forms the basis for multi-qubit gates. [0053] According to various embodiments of a quantum computer, individual particles (atoms/ions/molecules) can first be trapped in an array and arranged into particular configurations.
  • one or more particles are prepared in a desired quantum state.
  • HQU-01325 HU 9348 Quantum circuits can then be implemented by a sequence of qubit operations acting on individual qubits (single-qubit gates) or on groups of two or more qubits (multi-qubit gates).
  • the state of the particles can be read out in order to observe the result of the quantum circuit.
  • the readout can be accomplished using an observation system that typically includes an electron-multiplied CCD (EMCCD) camera image to detect particles’ loaded positions, and a second camera image to read out the particles’ final states by, for example, detecting fluorescence emitted by the particles in their final states.
  • EMCCD electron-multiplied CCD
  • Quantum information platforms rely on interactions between qubits, either for performing quantum gates or for performing analog many-body simulation. Qubits often interact in a local way, however, which limits the connectivity of the circuit or the analog simulation and constrains the possible computations. While some platforms can communicate in a nonlocal way through the use of a shared bus (e.g., trapped ions), these shared-bus approaches are limited to small systems and thus still require a way to dynamically move qubits around in order to truly scale up the platform.
  • Neutral atom arrays can be dynamically reconfigured while preserving quantum coherence and entanglement between qubits, by storing quantum information in hyperfine states and shuttling atoms in optical tweezers.
  • ⁇ ⁇ ( ⁇ ) is a function HQU-01325 HU 9348 of the code size ⁇ , as ⁇ is a function of ⁇ . Assuming the idling errors ⁇ ⁇ ( ⁇ ) can also improve as the gate error ⁇ ⁇ improves: ⁇ ⁇ 0.005 Equation 4 where the coherence time ⁇ ⁇ and other constant parameters in ⁇ ⁇ ( ⁇ ) are listed above. [0139] Exemplary Methods [0140] Code constructions [0141] The following section focuses on two families of qLDPC codes, although it will be appreciated that these results may be extended to asymptotically good codes.
  • the first family of codes are hypergraph product (HGP) codes, formed from the product of two classical LDPC codes.
  • HGP hypergraph product
  • classical expander codes can be obtained asymptotically, for example, from random biregular Tanner graphs, and will have sufficient vertex expansion with high probability.
  • Logical operators are inherited from the underlying classical code, and one can choose a basis such that each logical qubit has support in only a single row or column.
  • HGP codes are constructed by taking the hypergraph product of classical LDPC codes defined by (3,4)-regular Tanner graphs, i.e., bipartite graphs with degree-3 bit nodes and degree-4 check nodes.
  • classical LDPC codes defined by (3,4)-regular Tanner graphs, i.e., bipartite graphs with degree-3 bit nodes and degree-4 check nodes.
  • a family of HGP codes is obtained with a constant encoding rate ⁇ ⁇ ⁇ 0.04.
  • the classical code is selected having the largest distance, Tanner graph girth larger than 6 (length of the shortest cycle in the Tanner graph, obtained through rejection sampling without performing edge swaps), and the largest spectral gap (the gap between the largest two singular values of the check matrices) from randomly generated instances.
  • the hypergraph product of vertex-expanding classical codes yields HGP codes that satisfy the syndrome confinement property, and support single-shot QEC.
  • the second family of codes considered are quasi-cyclic lifted product (LP) codes, which can be viewed as a hypergraph product code followed by a symmetry reduction to reduce the number of required qubits.
  • a quasi-cyclic LP code is obtained from HQU-01325 HU 9348 two base protographs (analogs of the classical codes in the HGP construction) associated with two base matrices ⁇ and ⁇ over the quotient pol R[ ⁇ ] ⁇ ⁇ ynomial ring
  • the two base matrices are of size ⁇ ⁇ ⁇ and ⁇ ⁇ ⁇ , respectively.
  • Equation 7 The ⁇ ( ⁇ ) check matrix ⁇ ⁇ ( ⁇ ⁇ ) is then obtained by replacing each entry of ⁇ ⁇ ( ⁇ ⁇ ) with its matrix representation as ⁇ by ⁇ circulant matrices, a process known as a lift.
  • the encoding rate is lower bounded by ⁇ [0147]
  • Fig.12 shows a LP code using a 3 by 5 protograph associated with a base matrix ⁇ ⁇
  • the checks and bits of the protograph are illustrated by the big dashed nodes.
  • the ⁇ -th dashed check node is connected to the ⁇ -th dashed bit node if ⁇ ⁇ is non-zero.
  • a lift of the protograph is done by replacing each dashed node with its two inner solid nodes, and setting up the connectivity between the inner nodes according to the matrix representation of each ring element ⁇ ⁇ .
  • Equation 7 corresponds to taking the hypergraph product between the HQU-01325 HU 9348 protograph and itself, obtaining a grid of dashed nodes.
  • the connectivity between the dashed nodes is inherited from ⁇ . Then the qubits and the quantum checks are given by the inner nodes after the lift, and their connectivity is given by the matrix representation of ⁇ ⁇ and ⁇ ⁇ .
  • An important feature of the LP codes is that they still have some remaining product structure even after the lift. As shown in Fig.12, when flattening the inner nodes vertically (horizontally), the vertical (horizontal) connectivity between the qubits and the checks for each column (row) is the same as the left (top) lifted classical code.
  • a base matrix of dimension 3 by 5 is chosen, where all entries have a single polynomial term, and a family of codes is obtained with sizes up to 1428 by increasing the lift size ⁇ from 16 to 42.
  • the classical parity checks are optimized by choosing the base matrix entries over the quotient polynomial ring to obtain the best classical distance for the particular lift size ⁇ .
  • the choice of the base matrix entries is also such that the girth is at least 8, and the distances of the lifted qLDPC codes match the designed classical distances with a high probability. Allowing multiple polynomial terms for each base matrix entry and more protographs of different sizes gives more flexibility in qLDPC code design and improves their distances.
  • the classical base matrices used to construct the four LP codes used in this example are provided below. Denoting ⁇ ⁇ ⁇ as a base matrix with a lift size ⁇ and a classical code distance ⁇ after the lift, the base matrices are Equation 8 HQU-01325 HU 9348 Equation 9 [0149]
  • the quantum code distances are upper bounded by the classical code distances of the above (lifted) base matrices. After extensive search for minimum-weight logical operators using a GAP package, these upper bounds appear to be tight.
  • Atom rearrangement algorithm [0151]
  • the reconfigurable atom array platform features efficient, parallel control and rearrangement of large numbers of qubits, enabling the implementation of long-range connected quantum processors.
  • optical tools such as crossed acousto- optic deflectors (AODs) can generate a rectangular grid of optical tweezers that can be reconfigured on the fly, allowing the control of large code blocks consisting of thousands of physical qubits with only a handful of classical controls.
  • AODs crossed acousto- optic deflectors
  • SLMs spatial light modulators
  • Figs.16A-D illustrate the efficient implementation of quantum LDPC codes with atom arrays.
  • Fig.16A is an illustration of an algorithm to perform an arbitrary log-depth rearrangement.
  • Fig.16B is an illustration of the HGP code, obtained as a product of two classical codes. Lines indicate that the parity check at the syndrome node involves the corresponding data node.
  • Figs.16C-D show the required connectivity implemented via parallel row permutations, followed by parallel column permutations.
  • the second component is the observation that the product structure of crossed AODs matches well with the product structure present in many qLDPC codes. Details of a syndrome extraction circuit for HGP codes are provided, based on this observation, in Algorithm 2 (Fig.14), which is referred to as the product coloration circuit, as it makes use of HQU-01325 HU 9348 coloration circuits for each of the component classical codes.
  • Algorithm 2 Fig.14
  • the use of the product coloration circuit as opposed to alternative coloration or cardinal circuits, is necessary to fully exploit the parallel rearrangement capabilities across rows and columns.
  • the native entangling gate set of current atom array systems is diagonal, so CZ gates and appropriate Hadamard rotations are used to perform syndrome extraction.
  • any pair of qubits that are within a certain radius (known as the blockade radius) of each other will execute a CZ gate, while any individual qubits will undergo an identity gate.
  • CNOT gates are used as the entangling gates in the simulations. This can be physically justified if the CZ gates are much noisier than the Hadamard gates.
  • the product coloration circuit separately extracts the ⁇ and ⁇ syndromes, each requiring both a horizontal and vertical step.
  • the product coloration circuit will have 4 ⁇ entangling layers.
  • the product coloration circuit can also be applied to the LP codes used herein. As shown in Fig.12, a LP code has the same product vertical (horizontal) connectivity as a HGP code when flattening the inner nodes vertically (horizontally). Thus, the same product coloration circuit can be applied to the LP codes with an extra step of flattening the inner codes in between establishing the horizontal/vertical connections.
  • a modification of the above circuit is provided in Algorithm 3 (Fig.15) and Figs.17A-B, which is referred to as the pipelined product coloration circuit.
  • the main challenge is to choose a gate ordering HQU-01325 HU 9348 such that the desired ⁇ and ⁇ syndromes are correctly extracted.
  • Figs.17A-B ordering of operations in pipelined syndrome extraction is illustrated.
  • Fig.17B is an illustration of a local circuit that data qubits and ancilla qubits of the same round see, with dashed lines indicating different circuit moments.
  • the syndrome extraction order is valid. Similar analysis can be performed for the commutation relations with the next round of ancilla qubits.
  • 87 Rb atoms are loaded from a magneto-optical trap into a backbone array of programmable optical tweezers generated by a spatial light modulator (SLM). Atoms are rearranged in parallel into defect-free target positions in this SLM backbone by additional optical tweezers generated from a crossed 2D acousto-optic deflector (AOD). Following the rearrangement procedure, selected atoms are transferred from the static SLM traps back into the mobile AOD traps, and then these mobile atoms are moved to their starting positions in HQU-01325 HU 9348 the quantum circuit. During this entire process, the atoms are cooled with polarization gradient cooling.
  • SLM spatial light modulator
  • AOD acousto-optic deflector
  • the crossed AOD system is composed of two independently controlled AODs (AA Opto Electronic DTSX-400) for ⁇ and ⁇ control of the beam positions.
  • Both AODs are driven by independent arbitrary waveforms which are generated by a dual-channel arbitrary waveform generator (AWG) (M4i.6631-x8 by Spectrum Instrumentation) and then amplified through independent MW amplifiers (Minicircuits ZHL-5W-1).
  • AMG arbitrary waveform generator
  • the time-domain arbitrary waveforms are composed of multiple frequency tones corresponding to the ⁇ and ⁇ positions of columns and rows, which are independently changed as a function of time for steering around the AOD-trapped atoms dynamically; the full ⁇ and ⁇ waveforms are calculated by adding together the time-domain profile of all frequency components with a given amplitude and phase for each component.
  • the positions of the AOD atoms at each gate location are programmed and then smoothly interpolate (with a cubic profile) the AOD frequencies as a function of time between gate positions.
  • the cubic profile enacts a constant jerk onto the atoms, which allows movement of roughly 5 ⁇ 10 ⁇ faster (without heating and loss) than if moving at a constant velocity (linear profile).
  • stretches, compressions, and translations of the AOD trap array are applied: i.e., the AOD rows and columns never cross each other in order to avoid atom loss and heating associated with two frequency components crossing each other.
  • the AOD tweezer intensity is homogenized throughout the whole atom trajectory in order to minimize dephasing induced by a time-varying magnitude of differential light shifts.
  • a reference camera is used in the image plane to gauge the intensity of each AOD tweezer at each gate location and homogenize by varying the amplitude of each frequency component; during motion between two locations the amplitude of each individual frequency component is interpolated.
  • the SLM tweezer light (830 nm) and the AOD tweezer light (828 nm) are generated by two separate, free-running Ti:sapphire lasers (M Squared, 18-W pump).
  • the SLM tweezers Projected through a 0.5 NA objective, the SLM tweezers have a waist of roughly ⁇ 900 ⁇ ( ⁇ 1000 ⁇ for AODs).
  • the trap depths are ⁇ 2 ⁇ ⁇ 16 ⁇ , with radial trap frequencies of ⁇ 2 ⁇ ⁇ 80 ⁇ , and when running quantum circuits the trap depths are ⁇ 2 ⁇ ⁇ 4 ⁇ , with radial trap frequencies of ⁇ 2 ⁇ ⁇ 40 ⁇ .
  • This Raman laser system is based on dispersive optics.
  • 795-nm light (Toptica TA pro, 1.8W) is phase- modulated by an electro-optic modulator (Qubig), which is driven by microwaves at 3.4 GHz (Stanford Research Systems SRS SG384) that are doubled to 6.8 GHz and amplified.
  • the laser phase modulation is converted to amplitude modulation for driving Raman transitions through use of a Chirped Bragg Grating (Optigrate).
  • IQ control of the SG384 is used for frequency and phase control of the microwaves, which are imprinted onto the laser amplitude modulation and thus give us direct frequency and phase control over the hyperfine qubit drive.
  • the Raman laser illuminates the atom plane from the side in a circularly polarized elliptical beam with waists of 40 ⁇ and 560 ⁇ on the thin axis and the tall axis, respectively, with a total average optical power of 150 ⁇ on the atoms.
  • the large vertical extent ensures ⁇ 1% inhomogeneity across the atoms, and shot-to-shot fluctuations in the laser intensity are also ⁇ 1%.
  • the Raman laser is operated at a blue-detuned intermediate- state detuning of 180 GHz, resulting in two-photon Rabi frequencies of 1 MHz and an estimated scattering error per ⁇ pulse of 7 ⁇ 10 ⁇ (i.e.
  • the transport sequences are accompanied with dynamical decoupling sequences.
  • the number of pulses used is a tradeoff between preserving qubit coherence while minimizing pulse errors.
  • the CPMG-BB1 HQU-01325 HU 9348 sequence is more robust to amplitude errors but incurs more scattering error.
  • the sequence may be empirically optimized for any given experiment by choosing between these different sequences and a variable number of decoupling ⁇ pulses, optimizing on either single-qubit coherence (including the movement) or the final signal.
  • decoupling sequences are composed of a total 12-18 ⁇ pulses.
  • the average vibrational quantum number increase ⁇ is given by Equation 10 where ⁇ ( ⁇ ) is the Fourier transform of ⁇ ( ⁇ ) evaluated at the trap frequency ⁇ , and the zero point size of the particle ⁇ ⁇ ⁇ /(2 ⁇ ). ⁇ is the same for all initial levels of the oscillator.
  • Equation 11 is now compared to experimental observations. Atom loss is observed with movement of 55 ⁇ m in 200 ⁇ under a constant negative jerk.
  • the two-qubit CZ gate is implemented by two global Rydberg pulses, with each pulse at detuning ⁇ and length ⁇ , and with a phase jump ⁇ between the two pulses.
  • the pulse parameters are chosen such that qubit pairs, adjacent and under the Rydberg blockade constraint, will return from the Rydberg state back to the hyperfine qubit manifold with a phase depending on the state of the other qubit.
  • This 420-induced-phase issue may be addressed by performing an echo sequence: after the CZ gate, the 1013-nm Rydberg laser is turned off, a Raman ⁇ pulse is applied, and then the 420-nm laser is pulsed again to cancel the phase induced by the 420 light during the CZ gate.
  • This method echoes out the 420-induced phase, but comes at a cost of a factor of two increase in the 420-induced scattering error, which is the dominant source of error in two-qubit CZ gates.
  • Echo between CZ gates To address these various issues, a Raman ⁇ pulse is performed between each CZ gate to echo out spurious gate-induced phases on the hyperfine qubit. This approach has several advantages.
  • the 420-induced phase is now cancelled by pairs of CZ gates, without explicitly applying additional 420-nm pulses to echo each individual CZ gate, thereby reducing the scattering error of the CZ gate in this work by a factor of approximately two.
  • This echo technique having reduced the scattering error incurred during each gate, roughly compensates the increased scattering rate incurred by spreading optical power over more space in 2D, thereby giving comparable gate fidelities to the two-qubit CZ gate fidelities of ⁇ 97.4(2)%.
  • the echo between CZ gates also cancels the intrinsic single-qubit phase of the CZ gate, removing errors in the calibration of this parameter, as well as canceling any other gate-induced spurious single-qubit phases such as a ⁇ 0.01 rad phase induced by pulsing the traps off for 500 ns for the two-qubit gate. In instances where the number of CZ gates is odd, the echo for the final CZ gate is performed. [0184] Sign of intermediate-state detuning. To further suppress the effect of the spurious, 420-induced phase, the 420-nm laser is operated to be red-detuned (by 2 GHz) from the 6 ⁇ ⁇ / ⁇ transition.
  • 1 ⁇ state are of the same HQU-01325 HU 9348 sign, minimizing the differential light shift, while for blue detunings ⁇ 6.8 ⁇ , the light shift on the
  • Sensitivity to axial trap oscillations [0186] In typical Rydberg excitation timescales with optical tweezers, the axial trap oscillation frequencies of several kHz are inconsequential. Here, with circuits running as long as 1.2 ms, with Rydberg pulses throughout, the axial trap oscillations can have important effects.
  • the axial oscillations cause the atoms to make oscillations in/out of the Rydberg beams: at estimated axial temperature of ⁇ 25 ⁇ and axial oscillation frequency of 6 ⁇ , an axial spread ⁇ ⁇ 1.3 ⁇ is esimated.
  • the effect of this positional spread is relatively small on the pulse parameters of the CZ gate, but can be significant on the sensitive 420-induced phase that should be canceled by echoing out the phase induced by CZ gates separated by ⁇ 200 ⁇ .
  • the dephasing due to the axial trap oscillations is significant.
  • the beam waist of the 420-nm laser is increased to 35 microns (while maintaining constant intensity) and the laser frequency is changed to be 2-GHz red-detuned, together resulting in a significant reduction in the dephasing associated with improper echoing of the 420-nm pulse.
  • Rydberg beam shaping and homogeneity [0188] The Rydberg beams are shaped into tophats of variable size through wavefront control using the phase profile on a spatial light modulator (SLM). This ability allows matching the height of the beam profile to the experiment zone size of any given experiment, thereby maximizing the 1013-nm light intensity and CZ gate fidelities.
  • SLM spatial light modulator
  • Coherent mapping protocol [0190] A coherent mapping protocol is provided to transfer a generic many-body state in the ⁇
  • a fast Raman ⁇ pulse is performed, leaving only 150 ns between ending the many-body Rydberg dynamics and beginning the Rydberg ⁇ pulse.

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Abstract

Une correction d'erreur quantique dans des réseaux d'atomes reconfigurables est décrite. Une pluralité de bits quantiques de données est fournie, chaque bit quantique de la pluralité de bits quantiques de données étant placé dans un piège correspondant. Une pluralité de bits quantiques auxiliaires est fournie, chaque bit quantique auxiliaire de la pluralité de bits quantiques auxiliaires étant placé dans un piège correspondant. La pluralité de bits quantiques de données et la pluralité de bits quantiques auxiliaires sont agencés en une pluralité de rangées et une pluralité de colonnes, formant ainsi un réseau. Une pluralité de permutations de la pluralité de rangées et de la pluralité de colonnes est effectuée, chaque permutation de la pluralité de permutations plaçant chaque bit quantique de la pluralité de bits quantiques de données dans un rayon d'interaction de l'un des bits quantiques auxiliaires de la pluralité de bits quantiques auxiliaires, formant ainsi une pluralité de paires proches. Après chaque permutation de la pluralité de permutations, une impulsion de commande globale est appliquée au réseau, appliquant ainsi une grille à chaque paire proche de la pluralité de paires proches, et codant ainsi une matrice de contrôle de parité entre la pluralité de bits quantiques auxiliaires et la pluralité de bits quantiques de données.
EP24914477.5A 2023-05-01 2024-04-30 Codes de contrôle de parité à faible densité quantique avec réseaux d'atomes reconfigurables Pending EP4705885A2 (fr)

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