Riverlane (United Kingdom)

We propose the X3Z3 Floquet code, a dynamical code with improved performance under biased noise compared to other Floquet codes. The enhanced performance is attributed to a simplified decoding problem resulting from a persistent stabiliser-product symmetry, which surprisingly exists in a code without constant stabilisers. Even if such a symmetry is allowed, we prove that general dynamical codes with two-qubit parity measurements cannot admit one-dimensional decoding graphs, a key feature responsible for the high performance of bias-tailored stabiliser codes. Despite this, our comprehensive simulations show that the symmetry of the X3Z3 Floquet code renders its performance under biased noise far better than several leading Floquet codes. To maintain high-performance implementation in hardware without native two-qubit parity measurements, we introduce ancilla-assisted bias-preserving parity measurement circuits. Our work establishes the X3Z3 code as a prime quantum error-correcting code, particularly for devices with reduced connectivity, such as the honeycomb and heavy-hexagonal architectures.

Quantum computers are growing at a rapid pace. Trends show that the current decade could be the one in which quantum computers deliver commercial value. Today's quantum computers are overwhelmed by errors. To unlock their massive potential, a significant reduction in errors is required. Several qubit technologies are under research, e.g. superconducting, neutral atoms, trapped ions, photons and silicon. For useful quantum computing on these qubit technologies, Quantum Error Correction (QEC) turns unreliable physical qubits into useful logical qubits. QEC requires solving a real-time, large data volume decoding problem that determines the effect of physical noise on the computation carried out on logical qubits. The nature of the decoding problem depends on the qubit technology, choice of QEC code and mode of quantum computation. These are actively researched subjects in the quantum computing world. Hardware-based decoders that use Field Programmable Gate Array (FPGA) or Application Specific Integrated Circuits (ASIC) technologies are the most promising solutions in terms of speed and scalability. However, the design methodology for these solutions typically suffers from long lead times and a lack of flexibility. We propose GridGenQ, a hardware design utility that automates part of the FPGA/ASIC design methodology for distributed QEC decoders. We show that with our novel solution, development time for such distributed hardware decoders can be reduced from several weeks to few minutes. This allows for fast prototyping of distributed decoder architectures to meet the requirements posed by a dynamic QEC landscape.

Abstract Solving Computational Fluid Dynamics (CFD) problems requires the inversion of a linear system of equations, which can be done using a quantum algorithm for matrix inversion.
 However, the number of shots required to measure the output of the system can be prohibitive and remove any advantage obtained by quantum computing.
 In this work we propose a scheme for measuring the output of a Quantum Singular Value Transform (QSVT) matrix inversion algorithm specifically for the CFD use case.
 We use a Quantum Signal Processing (QSP) based amplitude estimation algorithm and show how it can be combined with the QSVT matrix inversion algorithm.
 We perform a detailed resource estimation of the amount of computational resources required for a single iteration of amplitude estimation, and compare the costs of amplitude estimation with the cost of not doing amplitude estimation and measuring the whole wavefunction.
 We also propose a measurement scheme to reduce the number of amplitudes measured in the CFD example by focussing on large amplitudes only. We simulate the whole CFD loop, finding that thus measuring only a small number of the total amplitudes in the output vector still results in an acceptable level of overall error.

Floquet codes are an intriguing generalisation of stabiliser and subsystem codes, which can provide good fault-tolerant characteristics while benefiting from reduced connectivity requirements in hardware. A recent question of interest has been how to run Floquet codes on devices which have defective – and therefore unusable – qubits. This is an under-studied issue of crucial importance for running such codes on realistic hardware. To address this challenge, we introduce a new method of accommodating defective qubits on a wide range of two-dimensional Floquet codes, which requires no additional connectivity in the underlying quantum hardware, no modifications to the original Floquet code's measurement schedule, can accommodate boundaries, and is optimal in terms of the number of qubits and stabilisers removed. We numerically demonstrate that, using this method, the planar honeycomb code is fault tolerant up to a fabrication defect probability of ≈12%. We find the fault-tolerant performance of this code under defect noise is competitive with that of the surface code, despite its sparser connectivity. We finally propose multiple ways this approach can be adapted to the underlying hardware, through utilising any additional connectivity available, and treating defective auxiliary qubits separately to defective data qubits. Our work therefore serves as a guide for the implementation of Floquet codes in realistic quantum hardware.

Quantum error correction enables the preservation of logical qubits with a lower logical error rate than the physical error rate, with performance depending on the decoding method. Traditional decoding approaches rely on the binarization (“hardening”) of readout data, thereby ignoring valuable information embedded in the analog (“soft”) readout signal. We present experimental results showcasing the advantages of incorporating soft information into the decoding process of a distance-3 (d=3) bit-flip surface code with flux-tunable transmons. We encode each of the 16 computational states that make up the logical state |0L⟩, and protect them against bit-flip errors by performing repeated Z-basis stabilizer measurements. To infer the logical fidelity for the |0L⟩ state, we average across the 16 computational states and employ two decoding strategies: minimum-weight perfect matching and a recurrent neural network. Our results show a reduction of up to 6.8% in the extracted logical error rate with the use of soft information. Decoding with soft information is widely applicable, independent of the physical qubit platform, and could allow for shorter readout durations, further minimizing logical error rates. Published by the American Physical Society 2024

Quantum error correction enables the preservation of logical qubits with a lower logical error rate than the physical error rate, with performance depending on the decoding method. Traditional decoding approaches rely on the binarization ('hardening') of readout data, thereby ignoring valuable information embedded in the analog ('soft') readout signal. We present experimental results showcasing the advantages of incorporating soft information into the decoding process of a distancethree (d = 3) bit-flip surface code with transmons. We encode each of the 16 computational states that make up the logical state |0L⟩, and protect them against bit-flip errors by performing repeated Z-basis stabilizer measurements. To infer the logical fidelity for the |0L⟩ state, we average across the 16 computational states and employ two decoding strategies: minimum-weight perfect matching and a recurrent neural network. Our results show a reduction of up to 6.8% in the extracted logical error rate with the use of soft information. Decoding with soft information is widely applicable, independent of the physical qubit platform, and could allow for shorter readout durations, further minimizing logical error rates.

We introduce Ambiguity Clustering, a new decoder for general quantum low-density parity check codes. On the recently proposed bivariate bicycle codes we find an order of magnitude speedup compared to the state-of-the-art BP-OSD decoder with no reduction in logical fidelity at physically realistic error rates. In particular, a single-threaded CPU implementation of Ambiguity Clustering is fast enough to decode the 144-qubit Gross code in real time for neutral atom and trapped ion systems.

We simulate the logical Hadamard gate in the surface code under a circuit-level noise model, compiling it to a physical circuit on square-grid connectivity hardware. Our paper is the first to do this for a logical unitary gate on a quantum error-correction code. We consider two proposals, both via patch-deformation: one that applies a transversal Hadamard gate (i.e. a domain wall through time) to interchange the logical X and Z strings, and another that applies a domain wall through space to achieve this interchange. We explain in detail why they perform the logical Hadamard gate by tracking how the stabilisers and the logical operators are transformed in each quantum error-correction round. We optimise the physical circuits and evaluate their logical failure probabilities, which we find to be comparable to those of a quantum memory experiment for the same number of quantum error-correction rounds. We present syndrome-extraction circuits that maintain the same effective distance under circuit-level noise as under phenomenological noise. We also explain how a SWAP-quantum error-correction round (required to return the patch to its initial position) can be compiled to only four two-qubit gate layers. This can be applied to more general scenarios and, as a byproduct, explains from first principles how the "stepping" circuits of the recent Google paper \cite{McEwenBaconGidney} can be constructed.

Error corrected quantum computers have the potential to change the way we solve computational problems. Quantum error correction involves repeated rounds of carefully scheduled gates to measure the stabilisers of a code. A set of scheduling rules are typically imposed on the order of gates to ensure the circuit can be rearranged into an equivalent circuit that can be easily seen to measure the stabilisers. In this work, we ask what would happen if we break these rules and instead use circuit schedules that we describe as tangled. We find that tangling schedules generates long-range entanglement not accessible using nearest-neighbour two-qubit gates. Our tangled schedules method provide a new tool for building quantum error correction circuits and we explore applications to design new architectures for fault-tolerant quantum computers. Notably, we show that, for the widely used Pauli-based model of computation (achieved by lattice surgery), this access to longer-range entanglement can reduce the device connectivity requirements, without compromising on circuit depth.