arXiv subjects

Simon C. Benjamin

Publications and source records attributed to Simon C. Benjamin.

At least 19 recordsLinked to original sources

arXiv2026

Stream Decoding with Confidence Scores at Room and Cryogenic Temperatures

In fault-tolerant quantum computing, fast and accurate decoding is crucial. Snowflake is a decoder for the surface code that runs in a streaming fashion. In this paper, we implement Snowflake on commercial FPGAs and validate them at room and cryogenic temperatures. Our results demonstrate high decoding throughput for small code distances that, when extrapolated, remains within acceptable limits for larger distances. Further, we incorporate the calculation of certain decoder confidence scores with negligible overhead both in terms of latency and physical resource utilisation. We note that implementing a large-scale system would require either a large FPGA beyond today's technology or clusters of FPGAs connected via a high-speed bus. Thus, we discuss an alternative architecture that exploits the locality of Snowflake by processing 2D slices of the 3D decoding window and offloading segments of the 3D structure to a high-speed memory.

quant-ph↗

arXiv2026

A route to damage tolerance exceeding $10\%$ in shuttling-equipped quantum processors

This is a short study of an approach offering high tolerance to damage (i.e. defects or 'drop outs') in solid state fault-tolerant quantum computing. Our method is primarily aimed at semiconductor electron spin-qubit systems, which have been shown to support fast and high-fidelity shuttling along pre-defined paths. We adapt the recent CAbLECAR method of Chadwick and Chong: stabilisers are performed by ancillas which each follow a bespoke pre-programmed path. We consider the simple surface code but we damage the physical lattice, and rely on route-solving software to find efficient pathways under constraints enforcing stabiliser commutation and hook error avoidance. Solutions are then converted to detector error models for Stim and logical error rates are obtained. We express our results by gauging the logical performance against that of a pristine lattice, using the notion of a reduced equivalent surface-code distance; for reasonable underlying error rates we find that $10\%$ damage leaves roughly half of the pristine equivalent distance ($d_\text{equiv}\approx0.48\,d_\text{pristine}$ in the large-array limit, rising to $\approx0.60$ for our smallest array). This suggests that one can tolerate substantial damage by building oversized arrays. We note that investigating damage tolerance of other qLDPC codes is a straightforward generalisation, and potentially one could adapt to damage emerging at runtime.

quant-ph↗

arXiv2025

Error mitigation for logical circuits using decoder confidence

Fault-tolerant quantum computers use decoders to monitor for errors and find a plausible correction. A decoder may provide a decoder confidence score (DCS) to gauge its success. We adopt a swim distance DCS, computed from the shortest path between syndrome clusters. By contracting tensor networks, we compare its performance under phenomenological noise to the well-known complementary gap and find that both reliably estimate the logical error probability (LEP) in a decoding window. We explore ways to use this to mitigate the LEP in entire logical circuits. For shallow circuits, we just abort if any decoding window produces an exceptionally low DCS: for a distance-13 surface code under circuit-level noise, rejecting a mere 0.1% of possible DCS values improves the entire circuit's LEP by more than 5 orders of magnitude. For larger algorithms comprising up to billions of windows, DCS-based rejection remains effective for enhancing observable estimation. Moreover, one can use the DCS to assign each circuit's output a unique LEP, and use it as a basis for maximum likelihood estimation. This can reduce the effects of noise by an order of magnitude at no quantum cost; methods can be combined for further improvements.

quant-ph↗

arXiv2024

Artificial Intelligence for Quantum Computing

Artificial intelligence (AI) advancements over the past few years have had an unprecedented and revolutionary impact across everyday application areas. Its significance also extends to technical challenges within science and engineering, including the nascent field of quantum computing (QC). The counterintuitive nature and high-dimensional mathematics of QC make it a prime candidate for AI's data-driven learning capabilities, and in fact, many of QC's biggest scaling challenges may ultimately rest on developments in AI. However, bringing leading techniques from AI to QC requires drawing on disparate expertise from arguably two of the most advanced and esoteric areas of computer science. Here we aim to encourage this cross-pollination by reviewing how state-of-the-art AI techniques are already advancing challenges across the hardware and software stack needed to develop useful QC - from device design to applications. We then close by examining its future opportunities and obstacles in this space.

quant-ph↗

arXiv2024

Low Depth Phase Oracle Using a Parallel Piecewise Circuit

We explore the important task of applying a phase $\exp(i\,f(x))$ to a computational basis state $\left| x \right>$. The closely related task of rotating a target qubit by an angle depending on $f(x)$ is also studied. Such operations are key in many quantum subroutines, and frequently $f(x)$ can be well-approximated by a piecewise function; examples range from the application of diagonal Hamiltonian terms (such as the Coulomb interaction) in grid-based many-body simulation, to derivative pricing algorithms. Here we exploit a parallelisation of the piecewise approach so that all constituent elementary rotations are performed simultaneously, that is, we achieve a total rotation depth of one. Moreover, we explore the use of recursive catalyst `towers' to implement these elementary rotations efficiently. We find that strategies prioritising execution speed can achieve circuit depth as low as $O(\log{n}{+}\log{S})$ for a register of $n$ qubits and a piecewise approximation of $S$ sections (presuming prior preparation of enabling resource states), albeit total qubit count then scales with $S$. In the limit of multiple repetitions of the oracle, we find that catalyst tower approaches have an $O(S\cdot n)$ T-count.

quant-ph↗

arXiv2024

Robustness of electron charge shuttling: Architectures, pulses, charge defects and noise thresholds

In semiconductor-based quantum technologies, the capability to shuttle charges between components is profoundly enabling. We numerically simulated various "conveyor-belt" shuttling scenarios for simple Si/SiO2 devices, explicitly modelling the electron's wave function using grid-based split-operator methods and a time-dependent 2D potential (obtained from a Poisson solver). This allowed us to fully characterise the electron loss probability and excitation fraction. Remarkably, with as few as three independent electrodes the process can remain near-perfectly adiabatic even in the presence of pulse imperfection, nearby charge defects, and Johnson-Nyquist noise. Only a substantial density of charge defects, or defects at 'adversarial' locations, can catastrophically disrupt the charge shuttling. While we do not explicitly model the spin or valley degrees of freedom, our results from this charge propagation study support the conclusion that conveyor-belt shuttling is an excellent candidate for providing connectivity in semiconductor quantum devices.

cond-mat.mes-hall↗

arXiv2023

Actis: A Strictly Local Union-Find Decoder

Fault-tolerant quantum computing requires classical hardware to perform the decoding necessary for error correction. The Union-Find decoder is one of the best candidates for this. It has remarkably organic characteristics, involving the growth and merger of data structures through nearest-neighbour steps; this naturally suggests the possibility of its realisation using a lattice of simple processors with nearest-neighbour links. In this way the computational load can be distributed with near-ideal parallelism. Here we show for the first time that this strict (rather than partial) locality is practical, with a worst-case runtime $\mathcal O(d^3)$ and mean runtime subquadratic in the surface code distance $d$. A novel parity-calculation scheme is employed which can simplify previously proposed architectures, and our approach is optimised for circuit-level noise. We compare our local realisation with one augmented by long-range links; while the latter is of course faster, we note that local asynchronous logic could negate the difference.

quant-ph↗

arXiv2023

Distributed Simulation of Statevectors and Density Matrices

Classical simulation of quantum computers is an irreplaceable step in the design of quantum algorithms. Exponential simulation costs demand the use of high-performance computing techniques, and in particular distribution, whereby the quantum state description is partitioned between a network of cooperating computers - necessary for the exact simulation of more than approximately 30 qubits. Distributed computing is notoriously difficult, requiring bespoke algorithms dissimilar to their serial counterparts with different resource considerations, and which appear to restrict the utilities of a quantum simulator. This manuscript presents a plethora of novel algorithms for distributed full-state simulation of gates, operators, noise channels and other calculations in digital quantum computers. We show how a simple, common but seemingly restrictive distribution model actually permits a rich set of advanced facilities including Pauli gadgets, many-controlled many-target general unitaries, density matrices, general decoherence channels, and partial traces. These algorithms include asymptotically, polynomially improved simulations of exotic gates, and thorough motivations for high-performance computing techniques which will be useful for even non-distributed simulators. Our results are derived in language familiar to a quantum information theory audience, and our algorithms formalised for the scientific simulation community. We have implemented all algorithms herein presented into an isolated, minimalist C++ project, hosted open-source on Github with a permissive MIT license, and extensive testing. This manuscript aims both to significantly improve the high-performance quantum simulation tools available, and offer a thorough introduction to, and derivation of, full-state simulation techniques.

quant-ph↗

arXiv2023

Quantum computing is scalable on a planar array of qubits with fabrication defects

To successfully execute large-scale algorithms, a quantum computer will need to perform its elementary operations near perfectly. This is a fundamental challenge since all physical qubits suffer a considerable level of noise. Moreover, real systems are likely to have a finite yield, i.e. some non-zero proportion of the components in a complex device may be irredeemably broken at the fabrication stage. We present a threshold theorem showing that an arbitrarily large quantum computation can be completed with a vanishing probability of failure using a two-dimensional array of noisy qubits with a finite density of fabrication defects. To complete our proof we introduce a robust protocol to measure high-weight stabilizers to compensate for large regions of inactive qubits. We obtain our result using a surface code architecture. Our approach is therefore readily compatible with ongoing experimental efforts to build a large-scale quantum computer.

quant-ph↗

arXiv2023

The Virtual Quantum Device (VQD): A tool for detailed emulation of quantum computers

We present the Virtual Quantum Device (VQD) platform, a system based on the QuEST quantum emulator. Through the use of VQDs, non-expert users can emulate specific quantum computers with detailed error models, bespoke gate sets and connectivities. The platform boasts an intuitive interface, powerful visualisation, and compatibility with high-performance computation for effective testing and optimisation of complex quantum algorithms or ideas across a range of quantum computing hardware. We create and explore five families of VQDs corresponding to trapped ions, nitrogen-vacancy-centres, neutral atom arrays, silicon quantum dot spins, and superconducting devices. Each is highly configurable through a set of tailored parameters. We showcase the key characteristics of each virtual device, providing practical examples of the tool's usefulness and highlighting each device's specific attributes. By offering user-friendly encapsulated descriptions of diverse quantum hardware, the VQD platform offers researchers the ability to rapidly explore algorithms and protocols in a realistic setting; meanwhile hardware experts can create their own VQDs to compare with their experiments.

quant-ph↗

arXiv2023

Grid-based methods for chemistry simulations on a quantum computer

First quantized, grid-based methods for chemistry modelling are a natural and elegant fit for quantum computers. However, it is infeasible to use today's quantum prototypes to explore the power of this approach, because it requires a significant number of near-perfect qubits. Here we employ exactly-emulated quantum computers with up to 36 qubits, to execute deep yet resource-frugal algorithms that model 2D and 3D atoms with single and paired particles. A range of tasks is explored, from ground state preparation and energy estimation to the dynamics of scattering and ionisation; we evaluate various methods within the split-operator QFT (SO-QFT) Hamiltonian simulation paradigm, including protocols previously-described in theoretical papers as well as our own novel techniques. While we identify certain restrictions and caveats, generally the grid-based method is found to perform very well; our results are consistent with the view that first quantized paradigms will be dominant from the early fault-tolerant quantum computing era onward.

quant-ph↗

arXiv2022

Resource-frugal Hamiltonian eigenstate preparation via repeated quantum phase estimation measurements

The preparation of Hamiltonian eigenstates is essential for many applications in quantum computing; the efficiency with which this can be done is of key interest. A canonical approach exploits the quantum phase estimation (QPE) algorithm. We adopt ideas from variants of this method to implement a resource-frugal iterative scheme, and provide analytic bounds on the complexity (simulation time cost) for various cases of available information and tools. We propose and characterise an extension involving a modification of the target Hamiltonian to increase overall efficiency. The presented methods and bounds are then demonstrated by preparing the ground state of the Hamiltonians of LiH and H$_2$ in second quantisation; we report the performance of both ideal and noisy implementations using simulated quantum computers. Convergence is generally achieved much faster than the bounds suggest, while the qualitative features are validated.

quant-ph↗

arXiv2022

Exploiting subspace constraints and ab initio variational methods for quantum chemistry

Variational methods offer a highly promising route to exploiting quantum computers for chemistry tasks. Here we employ methods described in a sister paper to the present report, entitled ab initio machine synthesis of quantum circuits, in order to solve problems using adaptively evolving quantum circuits. Consistent with prior authors we find that this approach can outperform human-designed circuits such as the coupled-cluster or hardware-efficient ansätze, and we make comparisons for larger instances up to 14 qubits. Moreover we introduce a novel approach to constraining the circuit evolution in the physically relevant subspace, finding that this greatly improves performance and compactness of the circuits. We consider both static and dynamics properties of molecular systems. The emulation environments used is QuESTlink; all resources are open source and linked from this paper.

quant-ph↗

arXiv2022

Quantum Error Mitigation

For quantum computers to successfully solve real-world problems, it is necessary to tackle the challenge of noise: the errors which occur in elementary physical components due to unwanted or imperfect interactions. The theory of quantum fault tolerance can provide an answer in the long term, but in the coming era of `NISQ' machines we must seek to mitigate errors rather than completely remove them. This review surveys the diverse methods that have been proposed for quantum error mitigation, assesses their in-principle efficacy, and then describes the hardware demonstrations achieved to date. We identify the commonalities and limitations among the methods, noting how mitigation methods can be chosen according to the primary type of noise present, including algorithmic errors. Open problems in the field are identified and we discuss the prospects for realising mitigation-based devices that can deliver quantum advantage with an impact on science and business.

quant-ph↗

arXiv2022

Quantum natural gradient generalised to noisy and non-unitary circuits

Variational quantum algorithms are promising tools whose efficacy depends on their optimisation method. For noise-free unitary circuits, the quantum generalisation of natural gradient descent has been introduced and shown to be equivalent to imaginary time evolution: the approach is effective due to a metric tensor reconciling the classical parameter space to the device's Hilbert space. Here we generalise quantum natural gradient to consider arbitrary quantum states (both mixed and pure) via completely positive maps; thus our circuits can incorporate both imperfect unitary gates and fundamentally non-unitary operations such as measurements. We employ the quantum Fisher information (QFI) as the core metric in the space of density operators. A modification of the Error Suppression by Derangements (ESD) and Virtual Distillation (VD) techniques enables an accurate and experimentally-efficient approximation of the QFI via the Hilbert-Schmidt metric tensor using prior results on the dominant eigenvector of noisy quantum states. Our rigorous proof also establishes the fundamental observation that the geometry of typical noisy quantum states is (approximately) identical in either the Hilbert-Schmidt metric or as characterised by the QFI. In numerical simulations of noisy quantum circuits we demonstrate the practicality of our approach and confirm it can significantly outperform other variational techniques.

quant-ph↗

arXiv2022

Exploring ab initio machine synthesis of quantum circuits

Gate-level quantum circuits are often derived manually from higher level algorithms. While this suffices for small implementations and demonstrations, ultimately automatic circuit design will be required to realise complex algorithms using hardware-specific operations and connectivity. Here we explore methods for the ab initio creation of circuits within a machine, either a classical computer or a hybrid quantum-classical device. We consider a range of techniques including: methods for introducing new gate structures, optimisation of parameterised circuits and choices of cost functions, and efficient removal of low-value gates exploiting the quantum geometric tensor and other heuristics. Using these principles we tackle the tasks of automatic encoding of unitary processes and translation (recompilation) of a circuit from one form to another. Using emulated quantum computers with various noise-free gate sets we provide simple examples involving up to 10 qubits, corresponding to 20 qubits in the augmented space we use. Further applications of specific relevance to chemistry modelling are considered in a sister paper, 'Exploiting subspace constraints and ab initio variational methods for quantum chemistry'.

quant-ph↗

arXiv2022

Quantum Analytic Descent

Variational algorithms have particular relevance for near-term quantum computers but require non-trivial parameter optimisations. Here we propose Analytic Descent: Given that the energy landscape must have a certain simple form in the local region around any reference point, it can be efficiently approximated in its entirety by a classical model -- we support these observations with rigorous, complexity-theoretic arguments. One can classically analyse this approximate function in order to directly `jump' to the (estimated) minimum, before determining a more refined function if necessary. We derive an optimal measurement strategy and generally prove that the asymptotic resource cost of a `jump' corresponds to only a single gradient vector evaluation.

quant-ph↗

arXiv2022

Tailoring Term Truncations for Electronic Structure Calculations Using a Linear Combination of Unitaries

A highly anticipated use of quantum computers is the simulation of complex quantum systems including molecules and other many-body systems. One promising method involves directly applying a linear combination of unitaries (LCU) to approximate a Taylor series by truncating after some order. Here we present an adaptation of that method, optimized for Hamiltonians with terms of widely varying magnitude, as is commonly the case in electronic structure calculations. We show that it is more efficient to apply LCU using a truncation that retains larger magnitude terms as determined by an iterative procedure. We obtain bounds on the simulation error for this generalized truncated Taylor method, and for a range of molecular simulations, we report these bounds as well as exact numerical results. We find that our adaptive method can typically improve the simulation accuracy by an order of magnitude, for a given circuit depth.

quant-ph↗