Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2504.11240 · IEEE International Conference on Quantum Computing and Engineering (QCE)

A Deep Dive into the Interplay of Structured Quantum Peaked Circuits and Infinite Temperature Correlation Functions

Myeongsu Kim, Manas Sajjan, Sabre Kais

Published Aug 30, 2025• 0 citations
arXivHTMLPDF

Abstract

Random quantum circuits have been extensively explored for quantum supremacy demonstrations [1]–[4]. However, verifying their output distributions remains challenging [2], [5], [6]. Here, we propose the infinite-temperature correlation function (ITCF) as a physically meaningful observable for noisy intermediate-scale quantum (NISQ) devices one that can be extracted using engineered circuits rather than relying on fully random constructions. This is realized by leveraging peaked quantum states whose probability distributions are sharply peaked at specific outcomes due to constructive interference thus offering more efficient verifiability and stronger signal observability. Rather than using Haar-random states, which often yield vanishing signals through destructive interference, we construct purposefully biased quantum states using either Grover-based amplitude amplification or shallow structured circuits. These engineered states amplify contributions from relevant operator subspaces, enabling robust detection of non-zero ITCF values that would otherwise be suppressed under random-state sampling. Our results highlight a problem-specific state preparation framework that mitigates signal loss from random averaging and facilitates the detection of physically meaningful observables in NISQ devices. We also discuss future extensions to multiqubit observables, scrambling diagnostics, and variational circuit optimization, underscoring the broader potential of Peaked States for quantum simulation and verification.

DOI
10.1109/qce65121.2025.00220

Related papers

Predictive Structure Behind Rare Outcomes in Random Quantum Circuits

Myeongsu Kim, Travis Humble, Sabre Kais

Local random quantum circuits can occasionally produce unusually large output probabilities. However, the final output distribution containing such a peak does not by itself reveal how the peak formed during circuit evolution. We investigate whether states formed during circuit evolution carry structural signatures that predict subsequent peak formation. In numerical experiments, circuits selected for large terminal peaks exhibit stronger pairwise correlations and probability redistribution, together with lower bipartite entanglement and output entropy, than controls generated by the same random-circuit model. Their intermediate states retain higher fresh-peak event probability when the remaining gates are independently regenerated. Within an unconditioned ensemble, a fixed structural score computed from the initial circuit segment predicts new-peak probability. Averaged equally across n=8-16, a replay with equal numbers of remaining-circuit evaluations shows that score-based allocation yields 1.80 times as many peaks as uniform allocation and about 18% more than a fixed baseline based on probability concentration and redistribution. Randomizing relative phases while preserving computational-basis probabilities strongly attenuates the selected-state advantage, demonstrating a functional contribution from relative-phase organization. Controlled gate-selection tests further show that the identified structure can guide circuit construction to promote peak formation. Together, these results connect rare output events to intermediate-state structure with predictive and constructive value under finite-depth local dynamics.

quant-pharXiv:2609.17482•Sep 16, 2026•0 citations

Simulating Hydrodynamics on Noisy Intermediate-Scale Quantum Devices with Random Circuits

Jonas Richter, Arijeet Pal

In a recent milestone experiment, Google's processor Sycamore heralded the era of "quantum supremacy" by sampling from the output of (pseudo-)random circuits. We show that such random circuits provide tailor-made building blocks for simulating quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. Specifically, we propose an algorithm consisting of a random circuit followed by a trotterized Hamiltonian time evolution to study hydrodynamics and to extract transport coefficients in the linear response regime. We numerically demonstrate the algorithm by simulating the buildup of spatiotemporal correlation functions in one- and two-dimensional quantum spin systems, where we particularly scrutinize the inevitable impact of errors present in any realistic implementation. Importantly, we find that the hydrodynamic scaling of the correlations is highly robust with respect to the size of the Trotter step, which opens the door to reach nontrivial time scales with a small number of gates. While errors within the random circuit are shown to be irrelevant, we furthermore unveil that meaningful results can be obtained for noisy time evolutions with error rates achievable on near-term hardware. Our work emphasizes the practical relevance of random circuits on NISQ devices beyond the abstract sampling task.

arXiv:2012.02795•Physical Review Letters•Jun 8, 2021•48 citations

On verifiable quantum advantage with peaked circuit sampling

Scott Aaronson, Yuxuan Zhang

Over a decade after its proposal, the idea of using quantum computers to sample hard distributions has remained a key path to demonstrating quantum advantage. Yet a severe drawback remains: verification seems to require classical computation exponential in the system size, $n$. As an attempt to overcome this difficulty, we propose a new candidate for quantum advantage experiments with otherwise random "peaked circuits", i.e., quantum circuits whose outputs have high concentrations on a computational basis state. Naturally, the heavy output string can be used for classical verification. In this work, we analytically and numerically study an explicit model of peaked circuits, in which $τ_r$ layers of uniformly random gates are augmented by $τ_p$ layers of gates that are optimized to maximize peakedness. We show that getting $1/\text{poly}(n)$ peakedness from such circuits requires $τ_{p} = Ω((τ_r/n)^{0.19})$ with overwhelming probability. However, we also give numerical evidence that nontrivial peakedness is possible in this model -- decaying exponentially with the number of qubits, but more than can be explained by any approximation where the output of a random quantum circuit is treated as a Haar-random state. This suggests that these peaked circuits have the potential for future verifiable quantum advantage experiments. Our work raises numerous open questions about random peaked circuits, including how to generate them efficiently, and whether they can be distinguished from fully random circuits in classical polynomial time.

arXiv:2404.14493•Apr 22, 2024•2 citations

Authenticating Quantum Circuits Through Localized Noise Fingerprints

Gabrielle MacNeil, Sandeep Sunkavilli, Qiaoyan Yu

Quantum computing promises to outperform classical systems, yet today’s Noisy Intermediate-Scale Quantum (NISQ) devices remain limited by gate errors, decoherence, and hardware variability. These challenges are compounded by the lack of built-in mechanisms to verify that quantum circuits execute as intended, especially in an untrusted quantum computer. In this work, we define quantum noise as a diagnostic signal rather than a nuisance. We propose a novel authentication method that utilizes Total Variation Distance (TVD) calculated using quantum noise. TVD compares a quantum circuit output distribution with a trusted quantum noise fingerprint. TVD offers a localized, interpretable metric for detecting structural tampering, such as gate reordering or injection. To support fine-grained verification, we introduce the concept of diagnostic ancilla qubits, non-invasive observers embedded in the circuit that store local noise signatures for post-execution analysis. While still a forward-looking concept, this proposal enables circuit-level verification. Our approach combines gate-level noise modeling with lightweight integrity checks, offering a promising path toward secure and tamper-evident quantum computation.

•Oct 13, 2025•0 citations

Shallow instantaneous quantum polynomial-time circuits for generative modeling on noisy intermediate-scale quantum hardware

Oriol Balló-Gimbernat, Marcos Arroyo-Sánchez, Paula García-Molina +2 more

Generative modeling is one of the most promising applications of quantum machine learning, yet training and deploying Quantum Generative Models (QGMs) on near-term hardware remains effectively intractable due to prohibitive gradient estimation and implementation costs. We propose a resource-efficient approach based on shallow Instantaneous Quantum Polynomial-time (IQP) circuits that circumvents these bottlenecks by leveraging efficient classical training while retaining the guarantee of sampling hardness. To validate this approach, we formalize graph generation as a hierarchy of physical correlations, allowing us to map abstract data features, such as edge density and bipartiteness, directly to the quantum observables required to learn them. We validate our protocol through demonstrations both on real hardware (from $28$ to $153$ qubits) and simulations ($28$ qubits). Results show that while global structural features exhibit significant degradation beyond $91$ qubits, our models achieve high-precision reproduction of local correlations, even up to $153$ qubits. These findings establish shallow IQP circuits as a robust, scalable candidate for generative tasks on current Noisy Intermediate-Scale Quantum (NISQ) devices.

quant-pharXiv:2511.05267•Physical Review A•Nov 10, 2025•0 citations

Simulating hydrodynamics on NISQ devices with random circuits

Jonas Richter, Arijeet Pal

In a recent milestone experiment, Google's processor Sycamore heralded the era of supremacy by sampling from the output of (pseudo-)random circuits. We show that such random circuits provide tailor-made building blocks for simulating quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. Specifically, we propose an algorithm consisting of a random circuit followed by a trotterized Hamiltonian time evolution to study hydrodynamics and to extract transport coefficients in the linear response regime. We numerically demonstrate the algorithm by simulating the buildup of spatiotemporal correlation functions in one- and two-dimensional quantum spin systems, where we particularly scrutinize the inevitable impact of errors present in any realistic implementation. Importantly, we find that the hydrodynamic scaling of the correlations is highly robust with respect to the size of the Trotter step, which opens the door to reach nontrivial time scales with a small number of gates. While errors within the random circuit are shown to be irrelevant, we furthermore unveil that meaningful results can be obtained for noisy time evolutions with error rates achievable on near-term hardware. Our work emphasizes the practical relevance of random circuits on NISQ devices beyond the abstract sampling task.

•Dec 4, 2020•0 citations
Random quantum circuits have been extensively explored for quantum supremacy demonstrations [1]–[4]. However, verifying their output distributions remains challenging [2], [5], [6]. Here, we propose the infinite-temperature correlation function (ITCF) as a physically meaningful observable for noisy intermediate-scale quantum (NISQ) devices one that can be extracted using engineered circuits rather than relying on fully random constructions. This is realized by leveraging peaked quantum states whose probability distributions are sharply peaked at specific outcomes due to constructive interference thus offering more efficient verifiability and stronger signal observability. Rather than using Haar-random states, which often yield vanishing signals through destructive interference, we construct purposefully biased quantum states using either Grover-based amplitude amplification or shallow structured circuits. These engineered states amplify contributions from relevant operator subspaces, enabling robust detection of non-zero ITCF values that would otherwise be suppressed under random-state sampling. Our results highlight a problem-specific state preparation framework that mitigates signal loss from random averaging and facilitates the detection of physically meaningful observables in NISQ devices. We also discuss future extensions to multiqubit observables, scrambling diagnostics, and variational circuit optimization, underscoring the broader potential of Peaked States for quantum simulation and verification.
Local random quantum circuits can occasionally produce unusually large output probabilities. However, the final output distribution containing such a peak does not by itself reveal how the peak formed during circuit evolution. We investigate whether states formed during circuit evolution carry structural signatures that predict subsequent peak formation. In numerical experiments, circuits selected for large terminal peaks exhibit stronger pairwise correlations and probability redistribution, together with lower bipartite entanglement and output entropy, than controls generated by the same random-circuit model. Their intermediate states retain higher fresh-peak event probability when the remaining gates are independently regenerated. Within an unconditioned ensemble, a fixed structural score computed from the initial circuit segment predicts new-peak probability. Averaged equally across n=8-16, a replay with equal numbers of remaining-circuit evaluations shows that score-based allocation yields 1.80 times as many peaks as uniform allocation and about 18% more than a fixed baseline based on probability concentration and redistribution. Randomizing relative phases while preserving computational-basis probabilities strongly attenuates the selected-state advantage, demonstrating a functional contribution from relative-phase organization. Controlled gate-selection tests further show that the identified structure can guide circuit construction to promote peak formation. Together, these results connect rare output events to intermediate-state structure with predictive and constructive value under finite-depth local dynamics.
In a recent milestone experiment, Google's processor Sycamore heralded the era of "quantum supremacy" by sampling from the output of (pseudo-)random circuits. We show that such random circuits provide tailor-made building blocks for simulating quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. Specifically, we propose an algorithm consisting of a random circuit followed by a trotterized Hamiltonian time evolution to study hydrodynamics and to extract transport coefficients in the linear response regime. We numerically demonstrate the algorithm by simulating the buildup of spatiotemporal correlation functions in one- and two-dimensional quantum spin systems, where we particularly scrutinize the inevitable impact of errors present in any realistic implementation. Importantly, we find that the hydrodynamic scaling of the correlations is highly robust with respect to the size of the Trotter step, which opens the door to reach nontrivial time scales with a small number of gates. While errors within the random circuit are shown to be irrelevant, we furthermore unveil that meaningful results can be obtained for noisy time evolutions with error rates achievable on near-term hardware. Our work emphasizes the practical relevance of random circuits on NISQ devices beyond the abstract sampling task.
Over a decade after its proposal, the idea of using quantum computers to sample hard distributions has remained a key path to demonstrating quantum advantage. Yet a severe drawback remains: verification seems to require classical computation exponential in the system size, nnn. As an attempt to overcome this difficulty, we propose a new candidate for quantum advantage experiments with otherwise random "peaked circuits", i.e., quantum circuits whose outputs have high concentrations on a computational basis state. Naturally, the heavy output string can be used for classical verification. In this work, we analytically and numerically study an explicit model of peaked circuits, in which τrτ_rτr​ layers of uniformly random gates are augmented by τpτ_pτp​ layers of gates that are optimized to maximize peakedness. We show that getting 1/poly(n)1/\text{poly}(n)1/poly(n) peakedness from such circuits requires τp=Ω((τr/n)0.19)τ_{p} = Ω((τ_r/n)^{0.19})τp​=Ω((τr​/n)0.19) with overwhelming probability. However, we also give numerical evidence that nontrivial peakedness is possible in this model -- decaying exponentially with the number of qubits, but more than can be explained by any approximation where the output of a random quantum circuit is treated as a Haar-random state. This suggests that these peaked circuits have the potential for future verifiable quantum advantage experiments. Our work raises numerous open questions about random peaked circuits, including how to generate them efficiently, and whether they can be distinguished from fully random circuits in classical polynomial time.
Quantum computing promises to outperform classical systems, yet today’s Noisy Intermediate-Scale Quantum (NISQ) devices remain limited by gate errors, decoherence, and hardware variability. These challenges are compounded by the lack of built-in mechanisms to verify that quantum circuits execute as intended, especially in an untrusted quantum computer. In this work, we define quantum noise as a diagnostic signal rather than a nuisance. We propose a novel authentication method that utilizes Total Variation Distance (TVD) calculated using quantum noise. TVD compares a quantum circuit output distribution with a trusted quantum noise fingerprint. TVD offers a localized, interpretable metric for detecting structural tampering, such as gate reordering or injection. To support fine-grained verification, we introduce the concept of diagnostic ancilla qubits, non-invasive observers embedded in the circuit that store local noise signatures for post-execution analysis. While still a forward-looking concept, this proposal enables circuit-level verification. Our approach combines gate-level noise modeling with lightweight integrity checks, offering a promising path toward secure and tamper-evident quantum computation.
Generative modeling is one of the most promising applications of quantum machine learning, yet training and deploying Quantum Generative Models (QGMs) on near-term hardware remains effectively intractable due to prohibitive gradient estimation and implementation costs. We propose a resource-efficient approach based on shallow Instantaneous Quantum Polynomial-time (IQP) circuits that circumvents these bottlenecks by leveraging efficient classical training while retaining the guarantee of sampling hardness. To validate this approach, we formalize graph generation as a hierarchy of physical correlations, allowing us to map abstract data features, such as edge density and bipartiteness, directly to the quantum observables required to learn them. We validate our protocol through demonstrations both on real hardware (from 282828 to 153153153 qubits) and simulations (282828 qubits). Results show that while global structural features exhibit significant degradation beyond 919191 qubits, our models achieve high-precision reproduction of local correlations, even up to 153153153 qubits. These findings establish shallow IQP circuits as a robust, scalable candidate for generative tasks on current Noisy Intermediate-Scale Quantum (NISQ) devices.
In a recent milestone experiment, Google's processor Sycamore heralded the era of supremacy by sampling from the output of (pseudo-)random circuits. We show that such random circuits provide tailor-made building blocks for simulating quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. Specifically, we propose an algorithm consisting of a random circuit followed by a trotterized Hamiltonian time evolution to study hydrodynamics and to extract transport coefficients in the linear response regime. We numerically demonstrate the algorithm by simulating the buildup of spatiotemporal correlation functions in one- and two-dimensional quantum spin systems, where we particularly scrutinize the inevitable impact of errors present in any realistic implementation. Importantly, we find that the hydrodynamic scaling of the correlations is highly robust with respect to the size of the Trotter step, which opens the door to reach nontrivial time scales with a small number of gates. While errors within the random circuit are shown to be irrelevant, we furthermore unveil that meaningful results can be obtained for noisy time evolutions with error rates achievable on near-term hardware. Our work emphasizes the practical relevance of random circuits on NISQ devices beyond the abstract sampling task.