arXiv subjects

John M. Martyn

Publications and source records attributed to John M. Martyn.

14 recordsLinked to original sources

arXiv2026

Trading Imaginary Time for Randomness in Ground State Preparation

Imaginary-time evolution (ITE) is a foundational method for ground state preparation on quantum computers. However, because ITE is non-unitary, existing implementations incur a sample complexity and/or classical cost that scales exponentially with the target imaginary time $β$. Moreover, the state itself converges slower than the energy, making accurate estimation of arbitrary ground state observables even more expensive. In this work, we improve upon standard ITE by introducing twirled imaginary-time evolution (TITE), which pairs ITE with real-time evolution applied for a random duration drawn from a carefully designed distribution. We prove that this randomization quadratically suppresses the trace distance to the ground state, and thus also the error of arbitrary observables, which allows roughly half of the imaginary time to be replaced with real-time evolution ($β\mapsto β/2$) while maintaining the same level of accuracy. Because real-time evolution is unitary and does not incur an overhead in sample complexity or classical computation, this affords a quadratic reduction in the cost of any black-box ITE implementation, including Trotterization and quantum imaginary-time evolution. We demonstrate the efficiency of our algorithm in noisy circuit-level simulations of a non-integrable Ising chain, showing substantial improvements over standard ITE.

quant-ph↗

arXiv2026

FTCircuitBench: A Benchmark Suite for Fault-Tolerant Quantum Compilation and Architecture

Realizing large-scale quantum advantage is expected to require quantum error correction (QEC), making the compilation and optimization of logical operations a critical area of research. Logical computation imposes distinct constraints and operational paradigms that differ from those of the Noisy Intermediate-Scale Quantum (NISQ) regime, motivating the continued evolution of compilation tools. Given the complexity of this emerging stack, where factors such as gate decomposition precision and computational models must be co-designed, standardized benchmarks and toolkits are valuable for evaluating progress. To support this need, we introduce FTCircuitBench, which serves as: (1) a benchmark suite of impactful quantum algorithms, featuring pre-compiled instances in both Clifford+T and Pauli Based Computation models; (2) a modular end-to-end pipeline allowing users to compile and decompose algorithms for various fault-tolerant architectures, supporting both prebuilt and custom optimization passes; and (3) a toolkit for evaluating the impact of algorithms and optimization across the full compilation stack, providing detailed numerical analysis at each stage. FTCircuitBench is fully open-sourced and maintained on Github.

quant-ph↗

arXiv2026

Faster Quantum Monte Carlo Simulation by Random Compilation

Quantum Monte Carlo (QMC) algorithms are among the most powerful classical methods for simulating quantum systems, yet their accuracy is often limited by the systematic errors in the approximations used, such as Trotterization. Here we introduce randomly compiled quantum Monte Carlo (RC-QMC) as a general framework that suppresses these systematic errors by averaging over a family of approximations rather than relying on a single fixed one. This strategy is grounded in the concept of randomized compiling from quantum computing, which suppresses errors by sampling over quantum gates, at essentially no additional computational cost. Consequently, our framework achieves a computational advantage over standard QMC methods when estimating a target state to a desired level of accuracy. We illustrate this advantage on two key Monte Carlo algorithms: (1) path integral quantum Monte Carlo for estimating thermal states, and (2) the quantum trajectories method for simulating open system dynamics. In aggregate, these results represent a cross-fertilization of quantum and classical algorithms, are readily generalizable to other QMC methods, and suggest wider applications in classical simulation.

quant-ph↗

arXiv2026

Analytic Approach to Quantum Control Using Quantum Signal Processing

Realizing coherent quantum computation requires precise and robust manipulation of quantum systems through quantum control protocols. Most quantum control techniques rely on heuristic methods for designing the driving pulses that steer the system towards a target state. Such methods are often based on brute-force optimization and offer limited understanding of the solution landscape. In contrast, quantum algorithms offer a rich body of analytical methods with rigorous error guarantees for implementing unitary and non-unitary transformations, which suggests a promising direction for developing new approaches to quantum control. Among various such algorithms, quantum signal processing (QSP) has emerged as a powerful framework for quantum algorithm design, implementation, and optimization. However, its potential for quantum control remains largely unexplored. In this work, we establish QSP-Control, an analytical framework for quantum control of qubit-oscillator dynamics. We focus on dispersively coupled qubit-oscillator systems and employ the QSP formalism to mitigate unwanted nonlinear effects arising from cross-Kerr interactions. In addition, we develop constructions for precise manipulation of Fock states by designing Fock-state-selective operators, based on structural parallels between the Jaynes-Cummings interaction and QSP. These findings demonstrate how several practically relevant problems in quantum control can be mapped to forms amenable to QSP, offering both a systematic design framework and an interpretable perspective on quantum control.

quant-ph↗

arXiv2026

COMPAS: A Distributed Multi-Party SWAP Test for Parallel Quantum Algorithms

The limited number of qubits per chip remains a critical bottleneck in quantum computing, motivating the use of distributed architectures that interconnect multiple quantum processing units (QPUs). However, executing quantum algorithms across distributed systems requires careful co-design of algorithmic primitives and hardware architectures to manage circuit depth and entanglement overhead. We identify multivariate trace estimation as a key subroutine that is naturally suited for distribution, and broadly useful in tasks such as estimating Rényi entropies, virtual cooling and distillation, and certain applications of quantum signal processing. In this work, we introduce COMPAS, an architecture that realizes multivariate trace estimation across a multi-party network of interconnected modular and distributed QPUs by leveraging pre-shared entangled Bell pairs as resources. COMPAS adds only a constant depth overhead and consumes Bell pairs at a rate linear in circuit width, making it suitable for near-term hardware. Unlike other schemes, which must choose between asymptotic optimality in circuit depth or GHZ width, COMPAS achieves both at once. Additionally, we analyze network-level errors and simulate the effects of circuit-level noise on the architecture.

quant-ph↗

arXiv2025

Hybrid Oscillator-Qubit Quantum Processors: Instruction Set Architectures, Abstract Machine Models, and Applications

Quantum computing with discrete variable (DV, qubit) hardware is approaching the large scales necessary for computations beyond the reach of classical computers. However, important use cases such as quantum simulations of physical models containing bosonic modes, and quantum error correction are challenging for DV-only systems. Separately, hardware containing native continuous-variable (CV, oscillator) systems has received attention as an alternative approach, yet the universal control of such systems is non-trivial. In this work, we show that hybrid CV-DV hardware offers a great advantage in meeting these challenges, offering a powerful computational paradigm that inherits the strengths of both DV and CV processors. We provide a pedagogical introduction to CV-DV systems and the multiple abstraction layers needed to produce a full software stack connecting applications to hardware. We present a variety of new hybrid CV-DV compilation techniques, algorithms, and applications, including the extension of quantum signal processing concepts to CV-DV systems and strategies to simulate systems of interacting spins, fermions, and bosons. To facilitate the development of hybrid CV-DV processor systems, we introduce formal Abstract Machine Models and Instruction Set Architectures -- essential abstractions that enable developers to formulate applications, compile algorithms, and explore the potential of current and future hardware for realizing fault-tolerant circuits, modules, and processors. Hybrid CV-DV quantum computations are beginning to be performed in superconducting, trapped ion, and neutral atom platforms, and large-scale experiments are set to be demonstrated in the near future. We present a timely and comprehensive guide to this relatively unexplored yet promising approach to quantum computation and providing an architectural backbone to guide future development.

quant-ph↗

arXiv2025

Parallel Quantum Signal Processing Via Polynomial Factorization

Quantum signal processing (QSP) is a methodology for constructing polynomial transformations of a linear operator encoded in a unitary. Applied to an encoding of a state $ρ$, QSP enables the evaluation of nonlinear functions of the form $\text{tr}(P(ρ))$ for a polynomial $P(x)$, which encompasses relevant properties like entropies and fidelity. However, QSP is a sequential algorithm: implementing a degree-$d$ polynomial necessitates $d$ queries to the encoding, equating to a query depth $d$. Here, we reduce the depth of these property estimation algorithms by developing Parallel Quantum Signal Processing. Our algorithm parallelizes the computation of $\text{tr} (P(ρ))$ over $k$ systems and reduces the query depth to $d/k$, thus enabling a family of time-space tradeoffs for QSP. This furnishes a property estimation algorithm suitable for distributed quantum computers, and is realized at the expense of increasing the number of measurements by a factor $O( \text{poly}(d) 2^{O(k)} )$. We achieve this result by factorizing $P(x)$ into a product of $k$ smaller polynomials of degree $O(d/k)$, which are each implemented in parallel with QSP, and subsequently multiplied together with a swap test to reconstruct $P(x)$. We characterize the achievable class of polynomials by appealing to the fundamental theorem of algebra, and demonstrate application to canonical problems including entropy estimation and partition function evaluation.

quant-ph↗

arXiv2025

Toward Mixed Analog-Digital Quantum Signal Processing: Quantum AD/DA Conversion and the Fourier Transform

Signal processing stands as a pillar of classical computation and modern information technology, applicable to both analog and digital signals. Recently, advancements in quantum information science have suggested that quantum signal processing (QSP) can enable more powerful signal processing capabilities. However, the developments in QSP have primarily leveraged \emph{digital} quantum resources, such as discrete-variable (DV) systems like qubits, rather than \emph{analog} quantum resources, such as continuous-variable (CV) systems like quantum oscillators. Consequently, there remains a gap in understanding how signal processing can be performed on hybrid CV-DV quantum computers. Here we address this gap by developing a new paradigm of mixed analog-digital QSP. We demonstrate the utility of this paradigm by showcasing how it naturally enables analog-digital conversion of quantum signals -- specifically, the transfer of states between DV and CV quantum systems. We then show that such quantum analog-digital conversion enables new implementations of quantum algorithms on CV-DV hardware. This is exemplified by realizing the quantum Fourier transform of a state encoded on qubits via the free-evolution of a quantum oscillator, albeit with a runtime exponential in the number of qubits due to information theoretic arguments. Collectively, this work marks a significant step forward in hybrid CV-DV quantum computation, providing a foundation for scalable analog-digital signal processing on quantum processors.

eess.SP↗

arXiv2025

Halving the Cost of Quantum Algorithms with Randomization

Quantum signal processing (QSP) provides a systematic framework for implementing a polynomial transformation of a linear operator, and unifies nearly all known quantum algorithms. In parallel, recent works have developed randomized compiling, a technique that promotes a unitary gate to a quantum channel and enables a quadratic suppression of error (i.e., $ε\rightarrow O(ε^2)$) at little to no overhead. Here we integrate randomized compiling into QSP through Stochastic Quantum Signal Processing. Our algorithm implements a probabilistic mixture of polynomials, strategically chosen so that the average evolution converges to that of a target function, with an error quadratically smaller than that of an equivalent individual polynomial. Because nearly all QSP-based algorithms exhibit query complexities scaling as $O(\log(1/ε))$ -- stemming from a result in functional analysis -- this error suppression reduces their query complexity by a factor that asymptotically approaches $1/2$. By the unifying capabilities of QSP, this reduction extends broadly to quantum algorithms, which we demonstrate on algorithms for real and imaginary time evolution, phase estimation, ground state preparation, and matrix inversion.

quant-ph↗

arXiv2024

Hybrid Oscillator-Qubit Quantum Processors: Simulating Fermions, Bosons, and Gauge Fields

We develop a hybrid oscillator-qubit processor framework for quantum simulation of strongly correlated fermions and bosons that avoids the boson-to-qubit mapping overhead encountered in qubit hardware. This framework gives exact decompositions of particle interactions such as density-density terms and gauge-invariant hopping, as well as approximate methods based on the Baker-Campbell Hausdorff formulas including the magnetic field term for the $U(1)$ quantum link model in $(2+1)$D. We use this framework to show how to simulate dynamics using Trotterisation, perform ancilla-free partial error detection using Gauss's law, measure non-local observables, estimate ground state energies using a oscillator-qubit variational quantum eigensolver as well as quantum signal processing, and we numerically study the influence of hardware errors in circuit QED experiments. To show the advantages over all-qubit hardware, we perform an end-to-end comparison of the gate complexity for the gauge-invariant hopping term and find an improvement of the asymptotic scaling with the boson number cutoff $S$ from $\mathcal{O}(\log(S)^2)$ to $\mathcal{O}(1)$ in our framework as well as, for bosonic matter, a constant factor improvement of better than $10^4$. We also find an improvement from $\mathcal{O}(\log(S))$ to $\mathcal{O}(1)$ for the $U(1)$ magnetic field term. While our work focusses on an implementation in superconducting hardware, our framework can also be used in trapped ion, and neutral atom hardware. This work establishes digital quantum simulation with hybrid oscillator-qubit hardware as a viable and advantageous method for the study of qubit-boson models in materials science, chemistry, and high-energy physics.

quant-ph↗

arXiv2024

Fault-Tolerant Neural Networks from Biological Error Correction Codes

It has been an open question in deep learning if fault-tolerant computation is possible: can arbitrarily reliable computation be achieved using only unreliable neurons? In the grid cells of the mammalian cortex, analog error correction codes have been observed to protect states against neural spiking noise, but their role in information processing is unclear. Here, we use these biological error correction codes to develop a universal fault-tolerant neural network that achieves reliable computation if the faultiness of each neuron lies below a sharp threshold; remarkably, we find that noisy biological neurons fall below this threshold. The discovery of a phase transition from faulty to fault-tolerant neural computation suggests a mechanism for reliable computation in the cortex and opens a path towards understanding noisy analog systems relevant to artificial intelligence and neuromorphic computing.

cs.LG↗

arXiv2023

Variational Neural-Network Ansatz for Continuum Quantum Field Theory

Physicists dating back to Feynman have lamented the difficulties of applying the variational principle to quantum field theories. In non-relativistic quantum field theories, the challenge is to parameterize and optimize over the infinitely many $n$-particle wave functions comprising the state's Fock space representation. Here we approach this problem by introducing neural-network quantum field states, a deep learning ansatz that enables application of the variational principle to non-relativistic quantum field theories in the continuum. Our ansatz uses the Deep Sets neural network architecture to simultaneously parameterize all of the $n$-particle wave functions comprising a quantum field state. We employ our ansatz to approximate ground states of various field theories, including an inhomogeneous system and a system with long-range interactions, thus demonstrating a powerful new tool for probing quantum field theories.

quant-ph↗

arXiv2023

Efficient Fully-Coherent Quantum Signal Processing Algorithms for Real-Time Dynamics Simulation

Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the simulation of electronic dynamics, which plays an essential role in chemical reactions, non-equilibrium dynamics, and material design. These systems are often time-dependent, which requires that the corresponding simulation algorithm can be successfully concatenated with itself over different time intervals to reproduce the overall coherent quantum dynamics of the system. In this paper, we quantify such simulation algorithms by a property called fully-coherent: the algorithm succeeds with arbitrarily high success probability $1-δ$, while only requiring a single copy of the initial state. We subsequently develop fully-coherent simulation algorithms based on quantum signal processing (QSP), including a novel algorithm that circumvents the use of amplitude amplification while also achieving a query complexity additive in time $t$, $\ln(1/δ)$, and $\ln(1/ε)$ for error tolerance $ε$: $Θ\big( \|\mathcal{H}\| |t| + \ln(1/ε) + \ln(1/δ)\big)$. Furthermore, we numerically analyze these algorithms by applying them to the simulation of the spin dynamics of the Heisenberg model and the correlated electronic dynamics of an H$_2$ molecule. Since any electronic Hamiltonian can be mapped to a spin Hamiltonian, our algorithm can efficiently simulate time-dependent ab initio electronic dynamics in the circuit model of quantum computation. Accordingly, it is also our hope that the present work serves a bridge between QSP-based quantum algorithms and chemical dynamics, stimulating a cross-fertilization between these exciting fields.

quant-ph↗

arXiv2021

A Grand Unification of Quantum Algorithms

Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian simulation, which appear as subroutines for large families of composite quantum algorithms. A number of these quantum algorithms were recently tied together by a novel technique known as the quantum singular value transformation (QSVT), which enables one to perform a polynomial transformation of the singular values of a linear operator embedded in a unitary matrix. In the seminal GSLW'19 paper on QSVT [Gilyén, Su, Low, and Wiebe, ACM STOC 2019], many algorithms are encompassed, including amplitude amplification, methods for the quantum linear systems problem, and quantum simulation. Here, we provide a pedagogical tutorial through these developments, first illustrating how quantum signal processing may be generalized to the quantum eigenvalue transform, from which QSVT naturally emerges. Paralleling GSLW'19, we then employ QSVT to construct intuitive quantum algorithms for search, phase estimation, and Hamiltonian simulation, and also showcase algorithms for the eigenvalue threshold problem and matrix inversion. This overview illustrates how QSVT is a single framework comprising the three major quantum algorithms, thus suggesting a grand unification of quantum algorithms.

quant-ph↗