arXiv subjects

Raymond Laflamme

Publications and source records attributed to Raymond Laflamme.

At least 19 recordsLinked to original sources

arXiv2026

Distributions of Noisy Expectation Values over Sets of Measurement Operators

Expectation values of measurement operators, interpreted as measurement probabilities, arise frequently throughout quantum algorithms. When quantum states are randomly distributed, their expectation values are also randomly distributed. In this work, with the goal of understanding non-unitary dynamics, we generalize previous derivations for distributions of expectation values [Campos et al., Phys. Lett. A 377, 1854 (2013)] to the case of sets of measurement operators and random mixed quantum states within variable sized environments. Using combinatorics approaches, we derive expressions for their moments. We proceed to construct empirical distributions of simulated Haar random brickwork quantum circuits with local depolarizing noise, and compare their form to a proposed effective global-depolarizing-like model with variable effective noise scales and environment dimensions. The fitted effective distributions reproduce peak behaviour across circuit depths, noise scales, and system sizes, while deviations in the distribution tails arise from local noise effects. The fit effective model parameters are also shown to vary smoothly and consistently with circuit depth and noise scale. Finally, sets of non-symmetric measurement operators are shown to exhibit distinct multi-modal distributions relative to uni-modal distributions for symmetric measurement operators, opening up questions about their simulability.

quant-ph↗

arXiv2026

Scalable Simulation of Fermionic Encoding Performance on Noisy Quantum Computers

A compelling application of quantum computers with thousands of qubits is quantum simulation. Simulating fermionic systems is both a problem with clear real-world applications and a computationally challenging task. In order to simulate a system of fermions on a quantum computer, one has to first map the fermionic Hamiltonian to a qubit Hamiltonian. The most popular such mapping is the Jordan-Wigner encoding, which suffers from inefficiencies caused by the high weight of some encoded operators. As a result, alternative local encodings have been proposed that solve this problem at the expense of a constant factor increase in the number of qubits required. Some such encodings possess local stabilizers, i.e., Pauli operators that act as the logical identity on the encoded fermionic modes. A natural error mitigation approach in these cases is to measure the stabilizers and discard any run where a measurement returns a -1 outcome. Using a high-performance stabilizer simulator, we classically simulate the performance of a local encoding known as the Derby-Klassen encoding and compare its performance with the Jordan-Wigner encoding and the ternary tree encoding. Our simulations use more complex error models and significantly larger system sizes (up to $18\times18$) than in previous work. We find that the high sampling requirements of postselection methods with the Derby-Klassen encoding pose a limitation to its applicability in near-term devices and call for more encoding-specific circuit optimizations.

quant-ph↗

arXiv2025

Enabling Technologies for Scalable Superconducting Quantum Computing

Experiments with superconducting quantum processors have successfully demonstrated the basic functions needed for quantum computation and evidence of utility, albeit without a sizable array of error-corrected qubits. The realization of the full potential of quantum computing centers on achieving large scale fault-tolerant quantum computers. Science, engineering and industry advances are needed to robustly generate, sustain, and efficiently manipulate an exponentially large computational (Hilbert) space as well as supply the number and quality components needed for such a scaled system. In this article, we suggest critical areas of quantum system and ecosystem development, with respect to the handling and transmission of quantum information within and out of a cryogenic environment, that would accelerate the development of quantum computers based on superconducting circuits.

quant-ph↗

arXiv2025

Quantum Error Corrected Non-Markovian Metrology

Quantum metrology aims to maximize measurement precision on quantum systems, with a wide range of applications in quantum sensing. Achieving the Heisenberg limit (HL) - the fundamental precision bound set by quantum mechanics - is often hindered by noise-induced decoherence, which typically reduces achievable precision to the standard quantum limit (SQL). While quantum error correction (QEC) can recover the HL under Markovian noise, its applicability to non-Markovian noise remains less explored. In this work, we analyze a hidden Markov model in which a quantum probe, coupled to an inaccessible environment, undergoes joint evolution described by Lindbladian dynamics, with the inaccessible degrees of freedom serving as a memory. We derive generalized Knill-Laflamme conditions for the hidden Markov model and establish three types of sufficient conditions for achieving the HL under non-Markovian noise using QEC. Additionally, we demonstrate the attainability of the SQL when these sufficient conditions are violated, by analytical solutions for special cases and numerical methods for general scenarios. Our results not only extend prior QEC frameworks for metrology but also provide new insights into precision limits under realistic noise conditions.

quant-ph↗

arXiv2025

Stochastic Security as a Performance Metric for Quantum-enhanced Generative AI

Motivated by applications of quantum computers in Gibbs sampling from continuous real-valued functions, we ask whether such algorithms can provide practical advantages for machine learning models trained on classical data and seek measures for quantifying such impacts. In this study, we focus on deep energy-based models (EBM), as they require continuous-domain Gibbs sampling both during training and inference. In lieu of fault-tolerant quantum computers that can execute quantum Gibbs sampling algorithms, we use the Monte Carlo simulation of diffusion processes as a classical alternative. More specifically, we investigate whether long-run persistent chain Monte Carlo simulation of Langevin dynamics improves the quality of the representations achieved by EBMs. We consider a scheme in which the Monte Carlo simulation of a diffusion, whose drift is given by the gradient of the energy function, is used to improve the adversarial robustness and calibration score of an independent classifier network. Our results show that increasing the computational budget of Gibbs sampling in persistent contrastive divergence improves both the calibration and adversarial robustness of the model, suggesting a prospective avenue of quantum advantage for generative AI using future large-scale quantum computers.

cs.LG↗

arXiv2024

Characterization of overparametrization in the simulation of realistic quantum systems

Quantum computing devices require exceptional control of their experimental parameters to prepare quantum states and simulate other quantum systems. Classical optimization procedures used to find such optimal control parameters, have further been shown in idealized settings to exhibit different regimes of learning. Of interest in this work is the overparameterization regime, where for systems with a sufficient number of parameters, global optima for prepared state and compiled unitary fidelities may potentially be reached exponentially quickly. Here, we study the robustness of overparameterization phenomena in the presence of experimental constraints on the controls, such as bounding or sharing parameters across operators, as well as in the presence of noise inherent to experimental setups. We observe that overparameterization phenomena are resilient in these realistic settings at short times, however fidelities decay to zero past a critical simulation duration due to accumulation of either quantum or classical noise. This critical depth is found to be logarithmic in the scale of noise, and optimal fidelities initially increase exponentially with depth, before decreasing polynomially with depth, and with noise. Our results demonstrate that parameterized ansatze can mitigate entropic effects from their environment, offering tantalizing opportunities for their application and experimental realization in near term quantum devices.

quant-ph↗

arXiv2024

Thermodynamic Analysis of Algorithmic Cooling Protocols: Efficiency Metrics and Improved Designs

Algorithmic cooling (AC) protocols have been predominantly studied for their cooling capabilities, with limited attention paid to their thermodynamic properties. This work explores a novel perspective by analyzing a broad family of AC protocols from a thermodynamic standpoint. First, we give an in-depth review and formal classification of standard AC protocols. Leveraging the transfer matrix formalism, we achieve a consistent calculation of performance metrics, encompassing both cooling limits and target state evolution. We obtained a unification of these diverse cooling limits into a single, coherent mathematical expression, streamlining comparative analyses. Then, to assess the efficiency of coherent cooling protocols, we introduce two generic metrics: the coefficient of performance $K$ and the Landauer Ratio $R_L$, and establish a direct interrelation. Applying these metrics, we thoroughly evaluate selected AC protocols, highlighting their relative strengths. Finally, we propose improved versions of AC protocols that exhibit enhanced thermodynamic performance, achieving desired target temperatures with lower work inputs. This research contributes to a deeper understanding of AC protocols and provides valuable insights for designing efficient cooling strategies in various applications.

quant-ph↗

arXiv2023

Quantum Maps Between CPTP and HPTP

For an open quantum system to evolve under CPTP maps, assumptions are made on the initial correlations between the system and the environment. Hermitian-preserving trace-preserving (HPTP) maps are considered as the local dynamic maps beyond CPTP. In this paper, we provide a succinct answer to the question of what physical maps are in the HPTP realm by two approaches. The first is by taking one step out of the CPTP set, which provides us with Semi-Positivity (SP) TP maps. The second way is by examining the physicality of HPTP maps, which leads to Semi-Nonnegative (SN) TP maps. Physical interpretations and geometrical structures are studied for these maps. The non-CP SPTP maps $Ψ$ correspond to the quantum non-Markovian process under the CP-divisibility definition ($Ψ= Ξ\circ Φ^{-1}$, where $Ξ$ and $Φ$ are CPTP). When removing the invertibility assumption on $Φ$, we land in the set of SNTP maps. A by-product of set relations is an answer to the following question -- what kind of dynamics the system will go through when the previous dynamic $Φ$ is non-invertible. In this case, the only locally well-defined maps are in $SN\backslash SP$, they live on the boundary of $SN$. Otherwise, the non-local information will be irreplaceable in the system's dynamic. With the understanding of physical maps beyond CPTP, we prove that the current quantum error correction scheme is still sufficient to correct quantum non-Markovian errors. In some special cases, lack of complete positivity could provide us with more error correction methods with less overhead.

quant-ph↗

arXiv2023

Experimental Activation of Strong Local Passive States with Quantum Information

Strong local passivity is a property of multipartite quantum systems from which it is impossible to extract energy locally. Surprisingly, if the strong local passive state displays entanglement, it could be possible to locally activate energy density by adding classical communication between different partitions of the system, through so-called "quantum energy teleportation" protocols. Here, we report both the first experimental observation of local activation of energy density on an entangled state and the first realization of a quantum energy teleportation protocol using nuclear magnetic resonance on a bipartite quantum system.

quant-ph↗

arXiv2023

Protecting information via probabilistic cellular automata

Probabilistic cellular automata describe the dynamics of classical spin models, which, for sufficiently small temperature $T$, can serve as classical memory capable of storing information even in the presence of nonzero external magnetic field $h$. In this article, we study a recently-introduced probabilistic cellular automaton, the sweep rule, and map out a region of two coexisting stable phases in the $(T,h)$ plane. We also find that the sweep rule belongs to the weak two-dimensional Ising universality class. Our work is a step towards understanding how simple geometrically-local error-correction strategies can protect information encoded into complex noisy systems, such as topological quantum error-correcting codes.

cond-mat.stat-mech↗

arXiv2023

Towards responsible quantum technology, safeguarding, engaging and advancing Quantum R&D

The expected societal impact of quantum technologies (QT) urges us to proceed and innovate responsibly. This article proposes a conceptual framework for Responsible QT that seeks to integrate considerations about ethical, legal, social, and policy implications (ELSPI) into quantum R&D, while responding to the Responsible Research and Innovation dimensions of anticipation, inclusion, reflection and responsiveness. After examining what makes QT unique, we argue that quantum innovation should be guided by a methodological framework for Responsible QT, aimed at jointly safeguarding against risks by proactively addressing them, engaging stakeholders in the innovation process, and continue advancing QT (SEA). We further suggest operationalizing the SEA-framework by establishing quantum-specific guiding principles. The impact of quantum computing on information security is used as a case study to illustrate (1) the need for a framework that guides Responsible QT, and (2) the usefulness of the SEA-framework for QT generally. Additionally, we examine how our proposed SEA-framework for responsible innovation can inform the emergent regulatory landscape affecting QT, and provide an outlook of how regulatory interventions for QT as base-layer technology could be designed, contextualized, and tailored to their exceptional nature in order to reduce the risk of unintended counterproductive effects of policy interventions. Laying the groundwork for a responsible quantum ecosystem, the research community and other stakeholders are called upon to further develop the recommended guiding principles, and discuss their operationalization into best practices and real-world applications. Our proposed framework should be considered a starting point for these much needed, highly interdisciplinary efforts.

quant-ph↗

arXiv2022

NISQ: Error Correction, Mitigation, and Noise Simulation

Error-correcting codes were invented to correct errors on noisy communication channels. Quantum error correction (QEC), however, may have a wider range of uses, including information transmission, quantum simulation/computation, and fault-tolerance. These invite us to rethink QEC, in particular, about the role that quantum physics plays in terms of encoding and decoding. The fact that many quantum algorithms, especially near-term hybrid quantum-classical algorithms, only use limited types of local measurements on quantum states, leads to various new techniques called Quantum Error Mitigation (QEM). This work examines the task of QEM from several perspectives. Using some intuitions built upon classical and quantum communication scenarios, we clarify some fundamental distinctions between QEC and QEM. We then discuss the implications of noise invertibility for QEM, and give an explicit construction called Drazin-inverse for non-invertible noise, which is trace preserving while the commonly-used Moore-Penrose pseudoinverse may not be. Finally, we study the consequences of having an imperfect knowledge about the noise, and derive conditions when noise can be reduced using QEM.

quant-ph↗

arXiv2022

Algorithmic cooling for resolving state preparation and measurement errors in quantum computing

State preparation and measurement errors are commonly regarded as indistinguishable. The problem of distinguishing state preparation (SPAM) errors from measurement errors is important to the field of characterizing quantum processors. In this work, we propose a method to separately characterize SPAM errors using a novel type of algorithmic cooling protocol called measurement-based algorithmic cooling (MBAC). MBAC assumes the ability to perform (potentially imperfect) projective measurements on individual qubits, which is available on many modern quantum processors. We demonstrate that MBAC can significantly reduce state preparation error under realistic assumptions, with a small overhead that can be upper bounded by measurable quantities. Thus, MBAC can be a valuable tool not only for benchmarking near-term quantum processors, but also for improving the performance of quantum processors in an algorithmic manner.

quant-ph↗

arXiv2021

Independent State and Measurement Characterization for Quantum Computers

Correctly characterizing state preparation and measurement (SPAM) processes is a necessary step towards building reliable quantum processing units (QPUs). In this work, we discuss the subtleties behind separately measuring SPAM errors. We propose a protocol that can separately estimate SPAM errors, in the case where quantum gates are ideal. In the case where the quantum gates are imperfect, we derive bounds on the estimated SPAM error rates, based on gate error measures which can be estimated independently of SPAM processes. Our method shows that the gauge ambiguity in characterizing SPAM operations can be resolved, by assuming that there exists one qubit whose initial state is uncorrelated with other qubits in a QPU. We test the protocol on a publicly available five-qubit QPU and demonstrate its validity by comparing our results with simulations.

quant-ph↗

arXiv2021

Detecting violations of macrorealism when the original Leggett-Garg inequalities are satisfied

Macroscopic realism (MR) is the notion that a time-evolving system possesses definite properties, irrespective of past or future measurements. Quantum mechanical theories can, however, produce violations of MR. Most research to date has focused on a single set of conditions for MR, the Leggett-Garg inequalities (LGIs), and on a single data set, the "standard data set", which consists of single-time averages and second-order correlators of a dichotomic variable Q for three times. However, if such conditions are all satisfied, then where is the quantum behaviour? In this paper, we provide an answer to this question by considering expanded data sets obtained from finer-grained measurements and MR conditions on those sets. We consider three different situations in which there are violations of MR that go undetected by the standard LGIs. First, we explore higher-order LGIs on a data set involving third- and fourth-order correlators, using a spin-1/2 and spin-1 system. Second, we explore the pentagon inequalities (PIs) and a data set consisting of all possible averages and second-order correlators for measurements of Q at five times. Third, we explore the LGIs for a trichotomic variable and measurements made with a trichotomic operator to, again, identify violations for a spin-1 system beyond those seen with a single dichotomic variable. We also explore the regimes in which combinations of two and three-time LGIs can be satisfied and violated in a spin-1 system, extending recent work. We discuss the possible experimental implementation of all the above results.

quant-ph↗

arXiv2021

Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes

In this work, we develop the theory of quasi-exact fault-tolerant quantum (QEQ) computation, which uses qubits encoded into quasi-exact quantum error-correction codes ("quasi codes"). By definition, a quasi code is a parametric approximate code that can become exact by tuning its parameters. The model of QEQ computation lies in between the two well-known ones: the usual noisy quantum computation without error correction and the usual fault-tolerant quantum computation, but closer to the later. Many notions of exact quantum codes need to be adjusted for the quasi setting. Here we develop quasi error-correction theory using quantum instrument, the notions of quasi universality, quasi code distances, and quasi thresholds, etc. We find a wide class of quasi codes which are called valence-bond-solid codes, and we use them as concrete examples to demonstrate QEQ computation.

quant-ph↗

arXiv2021

Hybrid quantum-classical approach to enhanced quantum metrology

Quantum metrology plays a fundamental role in many scientific areas. However, the complexity of engineering entangled probes and the external noise raise technological barriers for realizing the expected precision of the to-be-estimated parameter with given resources. Here, we address this problem by introducing adjustable controls into the encoding process and then utilizing a hybrid quantum-classical approach to automatically optimize the controls online. Our scheme does not require any complex or intractable off-line design, and it can inherently correct certain unitary errors during the learning procedure. We also report the first experimental demonstration of this promising scheme for the task of finding optimal probes for frequency estimation on a nuclear magnetic resonance (NMR) processor. The proposed scheme paves the way to experimentally auto-search optimal protocol for improving the metrology precision.

quant-ph↗

arXiv2020

Quasi-exact quantum computation

We study quasi-exact quantum error correcting codes and quantum computation with them. A quasi-exact code is an approximate code such that it contains a finite number of scaling parameters, the tuning of which can flow it to corresponding exact codes, serving as its fixed points. The computation with a quasi-exact code cannot realize any logical gate to arbitrary accuracy. To overcome this, the notion of quasi-exact universality is proposed, which makes quasi-exact quantum computation a feasible model especially for executing moderate-size algorithms. We find that the incompatibility between universality and transversality of the set of logical gates does not persist in the quasi-exact scenario. A class of covariant quasi-exact codes is defined which proves to support transversal and quasi-exact universal set of logical gates for $SU(d)$. This work opens the possibility of quantum computation with quasi-exact universality, transversality, and fault tolerance.

quant-ph↗