arXiv subjects

Michael A. Perlin

Publications and source records attributed to Michael A. Perlin.

At least 19 recordsLinked to original sources

arXiv2026

Quantum codes from classical annealing

We introduce an adaptive simulated annealing algorithm to search for moderately-sized quantum error-correcting codes with high encoding rates and large distances. Our search targets two classes of stabilizer codes: (1) CSS codes, and (2) a subclass of CSS codes that we call ``self-dual with equivalent logicals'' (SWEL) codes, the latter of which which admit transversal implementations of logical Hadamard and phase gates that can be leveraged to construct fault-tolerant gate sets. The search is guided by an energy function that acts as a surrogate for the logical error rate in a code-capacity noise model, combining code distance with a count of minimum-weight logical operators to resolve the discrete plateaux that impede naïve distance optimization. For block lengths of up to $50$ physical qubits, our search finds state-of-the-art CSS and SWEL codes whose distances frequently meet or exceed the variants of the quantum Gilbert-Varshamov bound. In addition to providing favorable seed codes for fault-tolerant architectures based on code concatenation, the codes found in this work are promising candidates for high-rate code demonstrations on near-term quantum computing hardware.

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arXiv2026

Quantum Approximate Optimization of Integer Graph Problems and Surpassing Semidefinite Programming for Max-k-Cut

Quantum algorithms for binary optimization problems have been the subject of extensive study. However, the application of quantum algorithms to integer optimization problems remains comparatively unexplored. In this paper, we study the Quantum Approximate Optimization Algorithm (QAOA) applied to integer problems on graphs, with each integer variable encoded in a qudit. We derive a general iterative formula for depth-$p$ QAOA expectation on high-girth $d$-regular graphs of arbitrary size. The cost of evaluating the formula is exponential in the QAOA depth $p$ but does not depend on the graph size. Evaluating this formula for Max-$k$-Cut problem for $p\leq 4$, we identify parameter regimes ($k=3$ with degree $d \leq 10$ and $k=4$ with $d \leq 40$) in which QAOA outperforms the Frieze-Jerrum semi-definite programming (SDP) algorithm, which provides the best worst-case guarantee on the approximation ratio. To strengthen the classical baseline, we introduce a new heuristic algorithm based on the degree-of-saturation that achieves strong results on the \texttt{GSet} benchmark with quasi-linear runtime in the number of edges. It empirically outperforms both the Frieze-Jerrum algorithm and shallow-depth QAOA on regular graphs. Nevertheless, we provide numerical evidence that QAOA may overtake this heuristic at depth $p\leq 20$. Our results show that moving beyond binary to integer optimization problems can open up new avenues for quantum advantage.

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arXiv2026

Variational quantum state preparation within an entangle-rotate circuit framework for quantum-enhanced metrology in noisy systems

We investigate the generation of quantum states for precision metrology in noisy two-level systems. These states are obtained by optimizing a variational quantum circuit to maximize the quantum Fisher information (QFI) of the output state for a given decoherence rate and interaction Hamiltonian. The circuit architecture, inspired by twist-and-turn schemes, features a sequence of $n$ entangling layers, each consisting of entangling gates followed by a global rotation. We observe notable improvements in the QFI as the circuit layer depth increases, even for appreciable noise rates, demonstrating that our entangle-rotate architecture expands the accessible state space under realistic noise conditions. Our approach thus provides a general and efficient framework for generating quantum-enhanced sensing states. Our analysis extends to systems of power-law interactions spanning from all-to-all to nearest-neighbor interactions. We also analyze the capabilities of our circuit to prepare states for system sizes greater than $8$ qubits.

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arXiv2026

Fault-tolerant execution of error-corrected quantum algorithms

Scaling up quantum algorithms to tackle high-impact problems in science and industry requires quantum error correction and fault tolerance. While progress has been made in experimentally realizing error-corrected primitives, the end-to-end execution of logical quantum algorithms using only fault-tolerant (FT) components has remained out of reach. We demonstrate the FT and error-corrected execution of two quantum algorithms, the Quantum Approximate Optimization Algorithm (QAOA) and the Harrow-Hassidim-Lloyd (HHL) algorithm applied to the Poisson equation, on Quantinuum H2 and Helios trapped-ion quantum processors using the $[[7,1,3]]$ Steane code. For QAOA circuits on 5 and 6 logical qubits, we show performance improvements from increasing the number of QAOA layers and the number of $T$ gates used to approximate logical rotations, despite increased physical circuit complexity. We further show that QAOA circuits with up to 8 logical qubits and 9 logical $T$ gates perform similarly to unencoded circuits. For the largest QAOA circuits we run, with 12 logical (97 physical) qubits and 2132 physical two-qubit gates, we still observe better-than-random performance. Finally, we show that adding active QEC cycles and increasing the repeat-until-success limit of state preparation subroutines can improve the performance of a quantum algorithm, thereby demonstrating critical capabilities of scalable FT quantum computation. Our results are enabled by an FT logical $T$ gate implementation with an infidelity of $\sim 2.6(4)\times10^{-3}$ and dynamic circuits with measurement-dependent feedback. Our work demonstrates near-break-even performance of complex, error-corrected algorithmic quantum circuits using only FT components.

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arXiv2026

Digital signatures with classical shadows on near-term quantum computers

Quantum mechanics provides cryptographic primitives whose security is grounded in hardness assumptions independent of those underlying classical cryptography. However, existing proposals require low-noise quantum communication and long-lived quantum memory, capabilities which remain challenging to realize in practice. In this work, we introduce a quantum digital signature scheme that operates with only classical communication, using the classical shadows of states produced by random circuits as public keys. We provide theoretical and numerical evidence supporting the conjectured hardness of learning the private key (the circuit) from the public key (the shadow). A key technical ingredient enabling our scheme is an improved state-certification primitive that achieves higher noise tolerance and lower sample complexity than prior methods. We realize this certification by designing a high-rate error-detecting code tailored to our random-circuit ensemble and experimentally generating shadows for 32-qubit states using circuits with $\geq 80$ logical ($\geq 582$ physical) two-qubit gates, attaining 0.90 $\pm$ 0.01 fidelity. With increased number of measurement samples, our hardware-demonstrated primitives realize a proof-of-principle quantum digital signature, demonstrating the near-term feasibility of our scheme.

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arXiv2026

Q-CHOP: Quantum constrained Hamiltonian optimization

Combinatorial optimization problems that arise in science and industry typically have constraints. Yet the presence of constraints makes them challenging to tackle using both classical and quantum optimization algorithms. We propose a new quantum algorithm for constrained optimization, which we call quantum constrained Hamiltonian optimization (Q-CHOP). Our algorithm leverages the observation that for many problems, while the best solution is difficult to find, the worst feasible (constraint-satisfying) solution is known. The basic idea of Q-CHOP is to enforce a Hamiltonian constraint at all times, thereby restricting evolution to the subspace of feasible states, and slowly ``rotate'' an objective Hamiltonian to trace an adiabatic path from the worst feasible state to the best feasible state. Q-CHOP thereby assigns qualitatively distinct roles to the constraint and objective functions of a constrained optimization problem. We additionally propose a version of Q-CHOP that can start in any feasible state. Finally, we benchmark Q-CHOP against the commonly-used adiabatic algorithm of quantum annealing with an objective function that penalizes constraint violation, and find that Q-CHOP consistently performs significantly better on a wide range of problems, including textbook graph problems, knapsack problems, combinatorial auctions, and a real-world financial use case of bond exchange-traded fund basket optimization.

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arXiv2025

Compilation Pipeline for Predicting Algorithmic Break-Even in an Early-Fault-Tolerant Surface Code Architecture

Recent experimental progress in realizing surface code on hardware, including demonstrations of break-even logical memory on devices with up to hundreds of physical qubits, has materially advanced the prospects for fault-tolerant quantum computation. This progress creates urgency for the development of compilation workflows that directly target the forthcoming generation of devices with thousands of physical qubits, for which algorithm execution becomes practical. We develop a pipeline for compiling logical algorithms to physical circuits implementing lattice surgery on the surface code, and use this pipeline to identify the requirements for achieving algorithmic break-even -- where quantum error correction improves the performance of a quantum algorithm -- for two prominent quantum algorithms: the quantum approximate optimization algorithm (QAOA) and quantum phase estimation (QPE). Our pipeline integrates several open-source software tools, and leverages recent advances in error-aware unitary gate synthesis, high-fidelity magic state production, and the calculation of correlation surfaces in the surface code. We perform classical simulations of physical Clifford proxy circuits produced by our pipeline, and find that both 5-qubit QAOA and QPE can reach algorithmic break-even with 2517 physical qubits (surface code distance $d=11$) at physical error rates of $p=10^{-3}$, or 1737 physical qubits ($d=9$) at $p=5\times 10^{-4}$. Our work thereby identifies conditions for achieving algorithmic break-even with near-term quantum hardware and paves the way towards an end-to-end compiler for early-fault-tolerant surface code architectures.

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arXiv2025

Certified randomness amplification by dynamically probing remote random quantum states

Cryptography depends on truly unpredictable numbers, but physical sources emit biased or correlated bits. Quantum mechanics enables the amplification of imperfect randomness into nearly perfect randomness, but prior demonstrations have required physically co-located, loophole-free Bell tests, constraining the feasibility of remote operation. Here we realize certified randomness amplification across a network by dynamically probing large, entangled quantum states on Quantinuum's 98-qubit Helios trapped-ion quantum processor. Our protocol is secure even if the remote device acts maliciously or is compromised by an intercepting adversary, provided the samples are generated quickly enough to preclude classical simulation of the quantum circuits. We stream quantum gates in real time to the quantum processor, maintain quantum state coherence for $\approx 0.9$ seconds, and then reveal the measurement bases to the quantum processor only milliseconds before measurement. This limits the time for classical spoofing to 30 ms and constrains the location of hypothetical adversaries to a $4{,}500$ km radius. We achieve a fidelity of 0.586 on random circuits with 64 qubits and 276 two-qubit gates, enabling the amplification of realistic imperfect randomness with a low entropy rate into nearly perfect randomness.

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arXiv2025

Realization of a Quantum Streaming Algorithm on Long-lived Trapped-ion Qubits

Large classical datasets are often processed in the streaming model, with data arriving one item at a time. In this model, quantum algorithms have been shown to offer an unconditional exponential advantage in space. However, experimentally implementing such streaming algorithms requires qubits that remain coherent while interacting with an external data stream. In this work, we realize such a data-streaming model using Quantinuum Helios trapped-ion quantum computer with long-lived qubits that communicate with an external server. We implement a quantum pair sketch, which is the primitive underlying many quantum streaming algorithms, and use it to solve Hidden Matching, a problem known to exhibit a theoretical exponential quantum advantage in space. Furthermore, we compile the quantum streaming algorithm to fault-tolerant quantum architectures based on surface and bivariate bicycle codes and show that the quantum space advantage persists even with the overheads of fault-tolerance.

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arXiv2025

Tensor networks for quantum computing

In the rapidly evolving field of quantum computing, tensor networks serve as an important tool due to their multifaceted utility. In this paper, we review the diverse applications of tensor networks and show that they are an important instrument for quantum computing. Specifically, we summarize the application of tensor networks in various domains of quantum computing, including simulation of quantum computation, quantum circuit synthesis, quantum error correction and mitigation, and quantum machine learning. Finally, we provide an outlook on the opportunities and the challenges of the tensor-network techniques.

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arXiv2025

Threshold for Fault-tolerant Quantum Advantage with the Quantum Approximate Optimization Algorithm

Optimization is often cited as a promising application of quantum computers. However, the low degree of provable quantum speedups has led prior rigorous end-to-end resource analyses to conclude that a quantum computer is unlikely to surpass classical state-of-the-art on optimization problems under realistic assumptions. In this work, we compile and analyze the Quantum Approximate Optimization Algorithm (QAOA) combined with Amplitude Amplification (AA) applied to random 8-SAT at the satisfiability threshold. Our compilation involves careful optimization of circuits for Hamiltonian simulation, which may be of independent interest. We use the analytical scaling of the time-to-solution for QAOA identified by PRX Quantum 5, 030348 (2024) and find that with QAOA depth $p=623$, QAOA+AA achieves a crossover with state-of-the-art classical heuristics at 179 variables and 14.99 hours of runtime when executed on a surface-code-based fault-tolerant quantum computer with 73.91 million physical qubits, a physical error rate of $10^{-3}$, and a $1~μ$s code cycle time. Notably, we allow the classical solver to be parallelized as long as its total energy consumption is equal to that required for decoding in the surface code. We further show that this restriction on classical solver energy consumption can be relaxed given optimistic but plausible reductions in physical error rates and fault-tolerance overheads, enabling a crossover of 2.94 hours using 8.88 million physical qubits against a classical solver running on a supercomputer with $725,760$ CPU cores. These findings support the hypothesis that large-scale fault-tolerant quantum computers will be useful for optimization.

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arXiv2024

Programming an Optical Lattice Interferometer

Programming a quantum device describes the usage of quantum logic gates, agnostic of hardware specifics, to perform a sequence of operations with (typically) a computing or sensing task in mind. Such programs have been executed on digital quantum computers, which despite their noisy character, have shown the ability to optimize metrological functions, for example in the generation of spin squeezing and optimization of quantum Fisher information for signals manifesting as spin rotations in a quantum register. However, the qubits of these programmable quantum sensors are tightly spatially confined and therefore suboptimal for enclosing the kinds of large spacetime areas required for performing inertial sensing. In this work, we derive a set of quantum logic gates for a cold atom optical lattice interferometer that manipulates the momentum of atoms. Here, the operations are framed in terms of single qubit operations and mappings between qubit subspaces with internal levels given by the Bloch (crystal) eigenstates of the lattice. We describe how the quantum optimal control method of direct collocation is well suited for obtaining the modulation waveforms of the lattice which achieve these operations.

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arXiv2024

Circuit decompositions and scheduling for neutral atom devices with limited local addressability

Despite major ongoing advancements in neutral atom hardware technology, there remains limited work in systems-level software tailored to overcoming the challenges of neutral atom quantum computers. In particular, most current neutral atom architectures do not natively support local addressing of single-qubit rotations about an axis in the xy-plane of the Bloch sphere. Instead, these are executed via global beams applied simultaneously to all qubits. While previous neutral atom experimental work has used straightforward synthesis methods to convert short sequences of operations into this native gate set, these methods cannot be incorporated into a systems-level framework nor applied to entire circuits without imposing impractical amounts of serialization. Without sufficient compiler optimizations, decompositions involving global gates will significantly increase circuit depth, gate count, and accumulation of errors. No prior compiler work has addressed this, and adapting existing compilers to solve this problem is nontrivial. In this paper, we present an optimized compiler pipeline that translates an input circuit from an arbitrary gate set into a realistic neutral atom native gate set containing global gates. We focus on decomposition and scheduling passes that minimize the final circuit's global gate count and total global rotation amount. As we show, these costs contribute the most to the circuit's duration and overall error, relative to costs incurred by other gate types. Compared to the unoptimized version of our compiler pipeline, minimizing global gate costs gives up to 4.77x speedup in circuit duration. Compared to the closest prior existing work, we achieve up to 53.8x speedup. For large circuits, we observe a few orders of magnitude improvement in circuit fidelities.

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arXiv2024

Variational quantum state preparation for quantum-enhanced metrology in noisy systems

We investigate optimized quantum state preparation for quantum metrology applications in noisy environments. Using the QFI-Opt package, we simulate a low-depth variational quantum circuit (VQC) composed of a sequence of global rotations and entangling operations applied to a chain of qubits that are subject to dephasing noise. The parameters controlling the VQC are numerically optimized to maximize the quantum Fisher information, which characterizes the ultimate metrological sensitivity of a quantum state with respect to a global rotation. We find that regardless of the details of the entangling operation implemented in the VQC, the optimal quantum states can be broadly classified into a trio of qualitative regimes--cat-like, squeezed-like, and product states--associated with different dephasing rates. Our findings are relevant for designing optimal state-preparation strategies for next-generation quantum sensors exploiting entanglement, such as time and frequency standards and magnetometers, aimed at achieving state-of-the-art performance in the presence of noise and decoherence.

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arXiv2024

Quantum Circuit Cutting for Classical Shadows

Classical shadow tomography is a sample-efficient technique for characterizing quantum systems and predicting many of their properties. Circuit cutting is a technique for dividing large quantum circuits into smaller fragments that can be executed more robustly using fewer quantum resources. We introduce a divide-and-conquer circuit cutting method for estimating the expectation values of observables using classical shadows. We derive a general formula for making predictions using the classical shadows of circuit fragments from arbitrarily cut circuits, and provide the sample complexity analysis for the case when observables factorize across fragments. Then, we numerically show that our divide-and-conquer method outperforms traditional uncut shadow tomography when estimating high-weight observables that act non-trivially on many qubits, and discuss the mechanisms for this advantage.

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arXiv2024

Robust Quantum Sensing with Multiparameter Decorrelation

The performance of a quantum sensor is fundamentally limited by noise. This noise is particularly damaging when it becomes correlated with the readout of a target signal, caused by fluctuations of the sensor's operating parameters. These uncertainties limit sensitivity in a way that can be understood with multiparameter estimation theory. We develop a new approach, adaptable to any quantum platform, for designing robust sensing protocols that leverages multiparameter estimation theory and machine learning to decorrelate a target signal from fluctuating off-target (``nuisance'') parameters. Central to our approach is the identification of information-theoretic goals that guide a machine learning agent through an otherwise intractably large space of potential sensing protocols. As an illustrative example, we apply our approach to a reconfigurable optical lattice to design an accelerometer whose sensitivity is decorrelated from lattice depth noise. We demonstrate the effect of decorrelation on outcomes and Bayesian inferencing through statistical analysis in parameter space, and discuss implications for future applications in quantum metrology and computing.

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arXiv2024

Average circuit eigenvalue sampling on NISQ devices

Average circuit eigenvalue sampling (ACES) was introduced by Flammia in arXiv:2108.05803 as a protocol to characterize the Pauli error channels of individual gates across the device simultaneously. The original paper posed using ACES to characterize near-term devices as an open problem. This work advances in this direction by presenting a full implementation of ACES for real devices and deploying it to Superstaq arXiv:2309.05157, along with a device-tailored resource estimation obtained through simulations and experiments. Our simulations show that ACES is able to estimate one- and two-qubit non-uniform Pauli error channels to an average eigenvalue absolute error of under $0.003$ and total variation distance of under 0.001 between simulated and reconstructed probability distributions over Pauli errors with $10^5$ shots per circuit using 5 circuits of depth 14. The question of estimating general error channels through twirling techniques in real devices remains open, as it is dependent on a device's native gates, but simulations with the Clifford set show results in agreement with reported hardware data. Experimental results on IBM's Algiers and Osaka devices are presented, where we characterize their error channels as Pauli channels without twirling.

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arXiv2023

Fault-tolerant measurement-free quantum error correction with multi-qubit gates

Measurement-free quantum error correction (MFQEC) offers an alternative to standard measurement-based QEC in platforms with an unconditional qubit reset gate. We revisit the question of fault tolerance (FT) for a measurement-free variant of the Steane code that leverages multi-qubit gates and redundant syndrome extraction, finding previously overlooked phase-flip errors that undermine FT. We then construct a revised MFQEC circuit that is resistant to all single-qubit errors, but which nonetheless cannot tolerate certain correlated errors. In order to investigate FT systematically, we introduce an efficient method to classically simulate MFQEC circuits with (i) Clifford gates for syndrome extraction, (ii) syndrome-controlled Pauli operations for decoding, and (iii) a Pauli noise model. We thereby find a pseudothreshold of $\sim0.7\%$ for our revised MFQEC Steane code under a restricted noise model previously considered in the literature. We then relax noise model assumptions to identify general requirements for FT with multi-qubit gates, finding that existing multi-qubit neutral atom gates are incompatible with fault-tolerant syndrome extraction in a straightforward implementation of both measurement-based and measurement-free variants of the Steane code. Decomposing multi-qubit gates into two-qubit gates similarly spoils FT. Finally, we discuss the theoretical ingredients that are necessary to recover FT for MFQEC codes, including single-shot FT and a recent proposal by Heußen \textit{et al.}~[arXiv:2307.13296] to achieve FT by ``copying'' errors onto an ancilla register. By combining multi-qubit gates, redundant syndrome extraction, and copy-assisted FT, we construct a measurement-free and fault-tolerant variant of the Steane code with a pseudothreshold of $\sim0.1\%$.

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