Fault-tolerant Quantum Information Processing Research Articles

A scalable and fast artificial neural network syndrome decoder for surface codes

Surface code error correction offers a highly promising pathway to achieve scalable fault-tolerant quantum computing. When operated as stabilizer codes, surface code computations consist of a syndrome decoding step where measured stabilizer operators are used to determine appropriate corrections for errors in physical qubits. Decoding algorithms have undergone substantial development, with recent work incorporating machine learning (ML) techniques. Despite promising initial results, the ML-based syndrome decoders are still limited to small scale demonstrations with low latency and are incapable of handling surface codes with boundary conditions and various shapes needed for lattice surgery and braiding. Here, we report the development of an artificial neural network (ANN) based scalable and fast syndrome decoder capable of decoding surface codes of arbitrary shape and size with data qubits suffering from the depolarizing error model. Based on rigorous training over 50 million random quantum error instances, our ANN decoder is shown to work with code distances exceeding 1000 (more than 4 million physical qubits), which is the largest ML-based decoder demonstration to-date. The established ANN decoder demonstrates an execution time in principle independent of code distance, implying that its implementation on dedicated hardware could potentially offer surface code decoding times of O(μsec), commensurate with the experimentally realisable qubit coherence times. With the anticipated scale-up of quantum processors within the next decade, their augmentation with a fast and scalable syndrome decoder such as developed in our work is expected to play a decisive role towards experimental implementation of fault-tolerant quantum information processing.

Quantum Nondemolition Measurements with Optical Parametric Amplifiers for Ultrafast Universal Quantum Information Processing

Realization of a room-temperature ultrafast photon-number-resolving quantum nondemolition (QND) measurement would have significant implications for photonic quantum information processing, enabling, for example, deterministic quantum computation in discrete-variable architectures, but the requirement for strong coupling has hampered the development of scalable implementations. In this work, we propose and analyze a nonlinear-optical route to photon-number-resolving QND using quadratic (i.e., χ(2)) nonlinear interactions. We show that the coherent pump field driving a frequency-detuned optical parametric amplifier (OPA) experiences displacements conditioned on the number of signal Bogoliubov excitations. A measurement of the pump displacement thus provides a QND measurement of the signal Bogoliubov excitations, projecting the signal mode to a squeezed photon-number state. We then show how our nonlinear OPA dynamics can be utilized to deterministically generate Gottesman-Kitaev-Preskill states with only additional Gaussian resources, offering an all-optical route for fault-tolerant quantum information processing in continuous-variable systems. Finally, we place these QND schemes into a more traditional context by highlighting analogies between the frequency-detuned optical parametric oscillator and multilevel atom-cavity quantum electrodynamics systems by showing how continuous monitoring of the outcoupled pump quadrature induces conditional localization of the intracavity signal mode onto squeezed photon-number states. Our analysis suggests that our proposal may be viable in near-term χ(2) nonlinear nanophotonics, highlighting the rich potential of the OPA as a universal tool for ultrafast non-Gaussian quantum state engineering and quantum computation.Received 18 October 2022Accepted 8 March 2023DOI:https://doi.org/10.1103/PRXQuantum.4.010333Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum computationQuantum engineeringQuantum information processingQuantum information processing with continuous variablesQuantum opticsQuantum state engineeringSecond order nonlinear optical processesQuantum InformationAtomic, Molecular & Optical

Universal conductance fluctuations in nanoscale topological insulator devices

Topological materials are promising candidates in fault-tolerant quantum information processing architectures, making it essential to understand the dephasing mechanisms in these materials. Here, we investigate gated, nanoscale mesas fabricated on thin films of cadmium arsenide (Cd3As2), a three-dimensional Dirac semimetal that can be tuned into different topological phases. We observe two independent types of conductance oscillations, one as a function of the applied magnetic field and the other as a function of the gate voltage. Varying the dimensions of the nanostructures allows the discrimination of a variety of scenarios for similar oscillations previously reported in the literature. We conclude that the conductance oscillations are not a signature of topological boundary states per se, but rather are universal conductance fluctuations. These results broadly inform future interpretations of electronic quantum interference in mesoscopic devices made from topological materials.

Two-dimensional superconductors with intrinsic p-wave pairing or nontrivial band topology

Over the past fifteen years, tremendous efforts have been devoted to realizing topological superconductivity in realistic materials and systems, predominately propelled by their promising application potentials in fault-tolerant quantum information processing. In this article, we attempt to give an overview on some of the main developments in this field, focusing in particular on two-dimensional crystalline superconductors that possess either intrinsic p-wave pairing or nontrivial band topology. We first classify the three different conceptual schemes to achieve topological superconductor (TSC), enabled by real-space superconducting proximity effect, reciprocal-space superconducting proximity effect, and intrinsic TSC. Whereas the first scheme has so far been most extensively explored, the subtle difference between the other two remains to be fully substantiated. We then move on to candidate intrinsic or p-wave superconductors, including Sr2RuO4,UTe2,Pb3Bi, and graphene-based systems. For TSC systems that rely on proximity effects, the emphases are mainly on the coexistence of superconductivity and nontrivial band topology, as exemplified by transition metal dichalcogenides, cobalt pnictides, and stanene, all in monolayer or few-layer regime. The review completes with discussions on the three dominant tuning schemes of strain, gating, and ferroelectricity in acquiring one or both essential ingredients of the TSC, and optimizations of such tuning capabilities may prove to be decisive in our drive towards braiding of Majorana zero modes and demonstration of topological qubits.

Noise Reduction in Qubit Readout with a Two-Mode Squeezed Interferometer

Fault-tolerant quantum information processing with flawed qubits and gates requires highly efficient, quantum nondemolition qubit readout. In superconducting circuits, qubit readout using coherent light with fidelity above 99% has been achieved by using quantum limited parametric amplifiers such as the Josephson parametric converter (JPC). However, further improvement of such measurement faces many challenges, including the vacuum fluctuation of the coherent light that limits measurement fidelity. In this work we demonstrate dispersive qubit readout with a two-mode squeezed light interferometer formed by two JPCs. The first JPC generates two-mode squeezed vacuum at its output, which is coherently recombined by the second JPC after one branch is phase shifted and displaced by its interaction with the qubit-cavity system on that arm of the interferometer. We observe a 31% improvement in the power signal-to-noise ratio (SNR) of projective readout after replacing vacuum fluctuation in the readout cavity with two-mode squeezed vacuum containing on average one photon. This demonstrates a more efficient way of improving SNR than by increasing readout power. Furthermore, we investigate the quantum properties of the two-mode squeezed light in the system through weak measurement. Surprisingly, we find that tuning the interferometer to be less projective increases the measurement efficiency relative to the optimum setting for projective measurement. These enhancements may enable remote entanglement with lower efficiency components in a system with qubits in both arms of the interferometer.

Performance of Teleportation-Based Error-Correction Circuits for Bosonic Codes with Noisy Measurements

Bosonic quantum error-correcting codes offer a viable direction towards reducing the hardware overhead required for fault-tolerant quantum information processing. A broad class of bosonic codes, namely rotation-symmetric codes, can be characterized by their phase-space rotation symmetry. However, their performance has been examined to date only within an idealistic noise model. Here, we further analyze the error-correction capabilities of rotation-symmetric codes using a teleportation-based error-correction circuit. To this end, we numerically compute the average gate fidelity, including measurement errors into the noise model of the data qubit. Focusing on physical measurement models, we assess the performance of heterodyne and adaptive homodyne detection in comparison to the previously studied canonical phase measurement. This setting allows us to shed light on the role of different currently available measurement schemes when decoding the encoded information. We find that with the currently achievable measurement efficiencies in microwave optics, bosonic rotation codes undergo a substantial decrease in their break-even potential. In addition, we perform a detailed analysis of Gottesman-Kitaev-Preskill (GKP) codes using a similar error-correction circuit that allows us to analyze the effect of realistic measurement models on different codes. In comparison to RSB codes, we find for GKP codes an even greater reduction in performance together with a vulnerability to photon-number dephasing. Our results show that highly efficient measurement protocols constitute a crucial building block towards error-corrected quantum information processing with bosonic continuous-variable systems.

Fast multiqubit Rydberg geometric fan-out gates with optimal control technology

Practical quantum computation requires highly efficient implementation of quantum logic gates. The fan-out gate represents such a type of multiqubit controlled gate with one qubit controlling a number of target qubits. Recent efforts for fan-out gates using Rydberg atoms include adiabatic operations along with the dark-state dynamics of Rydberg states [M. Khazali and K. M\o{}lmer, Phys. Rev. X 10, 021054 (2020)] and implementation based on the asymmetric Rydberg-Rydberg interaction [J. T. Young et al., Phys. Rev. Lett. 127, 120501 (2021)]. Inspired by these advances, we propose a fast-operation scheme for geometric multiqubit fan-out gates, in which the target qubits can be executed with arbitrary operations based on the asymmetric Rydberg-Rydberg interaction and time-optimal control technology. One of the main favorable features of our scheme is its performance in a nonadiabatic way and with the time-optimal control technology, by which the shortest smooth geometric path is found. Another feature, that the target qubits could be executed with arbitrary geometric quantum operations, makes our scheme general and useful. Therefore, our scheme provides a promising alternative route toward scalable fault-tolerant quantum information processing based on Rydberg atoms.

Cost-optimal single-qubit gate synthesis in the Clifford hierarchy

For universal quantum computation, a major challenge to overcome for practical implementation is the large amount of resources required for fault-tolerant quantum information processing. An important aspect is implementing arbitrary unitary operators built from logical gates within the quantum error correction code. A synthesis algorithm can be used to approximate any unitary gate up to arbitrary precision by assembling sequences of logical gates chosen from a small set of universal gates that are fault-tolerantly performable while encoded in a quantum error-correction code. However, current procedures do not yet support individual assignment of base gate costs and many do not support extended sets of universal base gates. We analysed cost-optimal sequences using an exhaustive search based on Dijkstra’s pathfinding algorithm for the canonical Clifford+Tset of base gates and compared them to when additionally includingZ-rotations from higher orders of the Clifford hierarchy. Two approaches of assigning base gate costs were used. First, costs were reduced toT-counts by recursively applying aZ-rotation catalyst circuit. Second, costs were assigned as the average numbers of raw (i.e. physical level) magic states required to directly distil and implement the gates fault-tolerantly. We found that the average sequence cost decreases by up to54±3%when using theZ-rotation catalyst circuit approach and by up to33±2%when using the magic state distillation approach. In addition, we investigated observed limitations of certain assignments of base gate costs by developing an analytic model to estimate the proportion of sets ofZ-rotation gates from higher orders of the Clifford hierarchy that are found within sequences approximating random target gates.

Dephasing-Protected Scalable Holonomic Quantum Computation on a Rabi Lattice

Holonomic quantum computing has attracted much attention in achieving robust and high-fidelity quantum gates owing to its built-in noise-resilience features. Here in this work, we propose an experimentally feasible scheme to realize scalable nonadiabatic non-Abelian holonomic gates in Rabi lattices, where each building block favors ultrastrong coupling and accordingly is portrayed by a quantum Rabi model (QRM). The polariton states with the lowest two energies in the QRM effectively simulate a spin-half system and thus constitute a logical qubit. In contrast to the existing schemes of using ancillary levels, our holonomic operations are performed with the aid of neighboring QRMs acting as ancillary qubits. Employing the two-tone driving scheme onto the physical system, various noncommutable single-qubit and nontrivial two-qubit holonomic gates are applicable on the computational basis, in which all-resonant control is employed and this guarantees fast speed and consequently high fidelities. In addition, our scheme exhibits a unique advantage of being immune to dephasing noises as a result of intrinsic characteristics of the ultrastrong coupling and the QRM. Therefore, this scheme prompts the integration of ultrastrong coupling and geometric properties to mitigate the negative effect of errors and decoherence. Ultimately, holonomic quantum gates incorporated in QRMs with all-resonant control may enable reaching the accuracy threshold for scalable fault-tolerant quantum-information processing within and beyond the ultrastrong couping regime.

Testing a quantum error-correcting code on various platforms

Quantum error correction plays an important role in fault-tolerant quantum information processing. It is usually difficult to experimentally realize quantum error correction, as it requires multiple qubits and quantum gates with high fidelity. Here we propose a simple quantum error-correcting code for the detected amplitude damping channel. The code requires only two qubits. We implement the encoding, the channel, and the recovery on an optical platform, the IBM Q System, and a nuclear magnetic resonance system. For all of these systems, the error correction advantage appears when the damping rate exceeds some threshold. We compare the features of these quantum information processing systems used and demonstrate the advantage of quantum error correction on current quantum computing platforms.

Coherent spin-state transfer via Heisenberg exchange

Quantum information science has the potential to revolutionize modern technology by providing resource-efficient approaches to computing1, communication2 and sensing3. Although the physical qubits in a realistic quantum device will inevitably suffer errors, quantum error correction creates a path to fault-tolerant quantum information processing4. Quantum error correction, however, requires that individual qubits can interact with many other qubits in the processor. Engineering such high connectivity can pose a challenge for platforms such as electron spin qubits5, which naturally favour linear arrays. Here we present an experimental demonstration of the transmission of electron spin states via the Heisenberg exchange interaction in an array of spin qubits. Heisenberg exchange coupling-a direct manifestation of the Pauli exclusion principle, which prevents any two electrons with the same spin state from occupying the same orbital-tends to swap the spin states of neighbouring electrons. By precisely controlling the wavefunction overlap between electrons in a semiconductor quadruple quantum dot array, we generate a series of coherent SWAP operations to transfer both single-spin and entangled states back and forth in the array without moving any electrons. Because the process is scalable to large numbers of qubits, state transfer through Heisenberg exchange will be useful for multi-qubit gates and error correction in spin-based quantum computers.

Topological quantum walks: Theory and experiments

Inspired by recent breakthroughs with topological quantum materials, which pave the way to novel, high-efficiency, low-energy magnetoelectric devices and fault-tolerant quantum information processing, inter alia, topological quantum walks have emerged as an exciting topic in its own right, especially due to the theoretical and experimental simplifications this approach offers. Motivated by impressive progress in topological quantum walks, we provide a perspective on theoretical studies and experimental investigations of topological quantum walks focusing on current explorations of topological properties arising for single-walker quantum walks.

Scalable star-shaped architecture for universal spin-based nonadiabatic holonomic quantum computation

As one of the key steps to achieve fault-tolerant quantum-information processing, nonadiabatic holonomic quantum computation has so far been realized in a number of physical settings. However, in some physical systems, particularly spin-qubit systems (which are actively considered for the realization of quantum computers), the experimental challenges are undeniable, and the lack of a practically feasible and scalable scheme that supports universal holonomic quantum computation all in a single well-defined setup is still an issue. Here, we propose and discuss a scalable star-shaped architecture with promising feasibility, which may pave the way for the realization of universal (electron-)spin-based nonadiabatic holonomic quantum computation.

Micromotion-enabled improvement of quantum logic gates with trapped ions

The micromotion of ion crystals confined in Paul traps is usually considered an inconvenient nuisance, and is thus typically minimized in high-precision experiments such as high-fidelity quantum gates for quantum information processing (QIP). In this work, we introduce a particular scheme where this behavior can be reversed, making micromotion beneficial for QIP. We show that using laser-driven micromotion sidebands, it is possible to engineer state-dependent dipole forces with a reduced effect of off-resonant couplings to the carrier transition. This allows one, in a certain parameter regime, to devise entangling gate schemes based on geometric phase gates with both a higher speed and a lower error, which is attractive in light of current efforts towards fault-tolerant QIP. We discuss the prospects of reaching the parameters required to observe this micromotion-enabled improvement in experiments with current and future trap designs.

Strong algorithmic cooling in large star-topology quantum registers

Cooling the qubit into a pure initial state is crucial for realizing fault-tolerant quantum information processing. Here we envisage a star-topology arrangement of reset and computation qubits for this purpose. The reset qubits cool or purify the computation qubit by transferring its entropy to a heat bath with the help of a heat-bath algorithmic cooling procedure. By combining standard NMR methods with powerful quantum control techniques, we cool central qubits of two large star-topology systems, with 13 and 37 spins, respectively. We obtain polarization enhancements by a factor of over 24, and an associated reduction in the spin temperature from 298 K down to 12 K. Exploiting the enhanced polarization of computation qubit, we prepare combination coherences of orders up to 15. By benchmarking the decay of these coherences we investigate the underlying noise process. Further, we also cool a pair of computation qubits and subsequently prepare them in an effective pure state.

Tunable magnetic textures: From Majorana bound states to braiding

A versatile control of magnetic systems, widely used to store information, can also enable manipulating Majorana bounds states (MBS) and implementing fault-tolerant quantum information processing. The proposed platform relies on the proximity-induced superconductivity in a two-dimensional electron gas placed next to an array of magnetic tunnel junctions (MTJs). A change in the magnetization configuration in the MTJ array creates tunable magnetic textures thereby removing several typical requirements for MBS: strong spin-orbit coupling, applied magnetic field, and confinement by one-dimensional structures which complicates demonstrating non-Abelian statistics through braiding. Recent advances in fabricating two-dimensional epitaxial superconductor/semiconductor heterostructures and designing tunable magnetic textures support the feasibility of this novel platform for MBS.

High-fidelity entangling gate for double-quantum-dot spin qubits

Electron spins in semiconductors are promising qubits because their long coherence times enable nearly 109 coherent quantum gate operations. However, developing a scalable high-fidelity two-qubit gate remains challenging. Here, we demonstrate an entangling gate between two double-quantum-dot spin qubits in GaAs by using a magnetic field gradient between the two dots in each qubit to suppress decoherence due to charge noise. When the magnetic gradient dominates the voltage-controlled exchange interaction between electrons, qubit coherence times increase by an order of magnitude. Using randomized benchmarking, we measure single-qubit gate fidelities of ~ 99%, and through self-consistent quantum measurement, state, and process tomography, we measure an entangling gate fidelity of 90%. In the future, operating double quantum dot spin qubits with large gradients in nuclear-spin-free materials, such as Si, should enable a two-qubit gate fidelity surpassing the threshold for fault-tolerant quantum information processing.

Measurement-based quantum communication with resource states generated by entanglement purification

We investigate measurement-based quantum communication with noisy resource states that are generated by entanglement purification. We consider the transmission of encoded information via noisy quantum channels using a measurement-based implementation of encoding, error correction and decoding. We show that such an approach offers advantages over direct transmission, gate-based error correction and measurement-based schemes with direct generation of resource states. We analyze the noise structure of resource states generated by entanglement purification and show that a local error model, i.e. noise acting independently on all qubits of the resource state, is a good approximation in general, and provides an exact description for $GHZ$-states. The latter are resources for a measurement-based implementation of error correction codes for bit-flip or phase flip errors. This provides a first link between the recently found very high thresholds for fault-tolerant measurement-based quantum information processing based on local error models for resource states, to error thresholds for gate based computational models.

Repeated quantum error correction on a continuously encoded qubit by real-time feedback.

Reliable quantum information processing in the face of errors is a major fundamental and technological challenge. Quantum error correction protects quantum states by encoding a logical quantum bit (qubit) in multiple physical qubits. To be compatible with universal fault-tolerant computations, it is essential that states remain encoded at all times and that errors are actively corrected. Here we demonstrate such active error correction on a continuously protected logical qubit using a diamond quantum processor. We encode the logical qubit in three long-lived nuclear spins, repeatedly detect phase errors by non-destructive measurements, and apply corrections by real-time feedback. The actively error-corrected qubit is robust against errors and encoded quantum superposition states are preserved beyond the natural dephasing time of the best physical qubit in the encoding. These results establish a powerful platform to investigate error correction under different types of noise and mark an important step towards fault-tolerant quantum information processing.

Semiconductor-inspired design principles for superconducting quantum computing.

Superconducting circuits offer tremendous design flexibility in the quantum regime culminating most recently in the demonstration of few qubit systems supposedly approaching the threshold for fault-tolerant quantum information processing. Competition in the solid-state comes from semiconductor qubits, where nature has bestowed some very useful properties which can be utilized for spin qubit-based quantum computing. Here we begin to explore how selective design principles deduced from spin-based systems could be used to advance superconducting qubit science. We take an initial step along this path proposing an encoded qubit approach realizable with state-of-the-art tunable Josephson junction qubits. Our results show that this design philosophy holds promise, enables microwave-free control, and offers a pathway to future qubit designs with new capabilities such as with higher fidelity or, perhaps, operation at higher temperature. The approach is also especially suited to qubits on the basis of variable super-semi junctions.