arXiv subjects

Andrea Mari

Publications and source records attributed to Andrea Mari.

At least 19 recordsLinked to original sources

arXiv2025

Deep-learned error mitigation via partially knitted circuits for the variational quantum eigensolver

The variational quantum eigensolver (VQE) is generally regarded as a promising quantum algorithm for near-term noisy quantum computers. However, when implemented with the deep circuits that are in principle required for achieving a satisfactory accuracy, the algorithm is strongly limited by noise. Here, we show how to make VQE functional via a tailored error mitigation technique based on deep learning. Our method employs multilayer perceptrons trained on the fly to predict ideal expectation values from noisy outputs combined with circuit descriptors. Importantly, a circuit knitting technique with partial knitting is adopted to substantially reduce the classical computational cost of creating the training data. We also show that other popular general-purpose quantum error mitigation techniques do not reach comparable accuracies. Our findings highlight the power of deep-learned quantum error mitigation methods tailored to specific circuit families, and of the combined use of variational quantum algorithms and classical deep learning.

quant-ph↗

arXiv2025

Can gravity mediate the transmission of quantum information?

We propose an experiment to test the non-classicality of the gravitational interaction. We consider two optomechanical systems that are perfectly isolated, except for a weak gravitational coupling. If a suitable resonance condition is satisfied, an optical signal can be transmitted from one system to the other over a narrow frequency band, a phenomenon that we call gravitationally induced transparency. In this framework, the challenging problem of testing the quantum nature of gravity is mapped to the easier task of determining the non-classicality of the gravitationally-induced optical channel: If the optical channel is not entanglement-breaking, then gravity must have a quantum nature. This approach is applicable without making any assumption on the, currently unknown, correct model of gravity in the quantum regime. In the second part of this work, we model gravity as a quadratic Hamiltonian interaction (e.g. a weak Newtonian force), resulting in a Gaussian thermal attenuator channel between the two systems. Depending on the strength of thermal noise, the system presents a sharp transition from an entanglement-breaking to a non-classical channel capable not only of entanglement preservation but also of asymptotically perfect quantum communication.

quant-ph↗

arXiv2024

Synergy between noisy quantum computers and scalable classical deep learning

We investigate the potential of combining the computational power of noisy quantum computers and of classical scalable convolutional neural networks (CNNs). The goal is to accurately predict exact expectation values of parameterized quantum circuits representing the Trotter-decomposed dynamics of quantum Ising models. By incorporating (simulated) noisy expectation values alongside circuit structure information, our CNNs effectively capture the underlying relationships between circuit architecture and output behaviour, enabling predictions for circuits with more qubits than those included in the training set. Notably, thanks to the quantum information, our CNNs succeed even when supervised learning based only on classical descriptors fails. Furthermore, they outperform a popular error mitigation scheme, namely, zero-noise extrapolation, demonstrating that the synergy between quantum and classical computational tools leads to higher accuracy compared with quantum-only or classical-only approaches. By tuning the noise strength, we explore the crossover from a computationally powerful classical CNN assisted by quantum noisy data, towards rather precise quantum computations, further error-mitigated via classical deep learning.

quant-ph↗

arXiv2024

Open Hardware Solutions in Quantum Technology

Quantum technologies such as communications, computing, and sensing offer vast opportunities for advanced research and development. While an open-source ethos currently exists within some quantum technologies, especially in quantum computer programming, we argue that there are additional advantages in developing open quantum hardware (OQH). Open quantum hardware encompasses open-source software for the control of quantum devices in labs, blueprints and open-source toolkits for chip design and other hardware components, as well as openly-accessible testbeds and facilities that allow cloud-access to a wider scientific community. We provide an overview of current projects in the OQH ecosystem, identify gaps, and make recommendations on how to close them today. More open quantum hardware would accelerate technology transfer to and growth of the quantum industry and increase accessibility in science.

physics.app-ph↗

arXiv2024

Quantum error mitigation by layerwise Richardson extrapolation

A widely used method for mitigating errors in noisy quantum computers is Richardson extrapolation, a technique in which the overall effect of noise on the estimation of quantum expectation values is captured by a single parameter that, after being scaled to larger values, is eventually extrapolated to the zero-noise limit. We generalize this approach by introducing \emph{layerwise Richardson extrapolation (LRE)}, an error mitigation protocol in which the noise of different individual layers (or larger chunks of the circuit) is amplified and the associated expectation values are linearly combined to estimate the zero-noise limit. The coefficients of the linear combination are analytically obtained from the theory of multivariate Lagrange interpolation. LRE leverages the flexible configurational space of layerwise unitary folding, allowing for a more nuanced mitigation of errors by treating the noise level of each layer of the quantum circuit as an independent variable. We provide numerical simulations demonstrating scenarios where LRE achieves superior performance compared to traditional (single-variable) Richardson extrapolation.

quant-ph↗

arXiv2023

Counting collisions in random circuit sampling for benchmarking quantum computers

We show that counting the number of collisions (re-sampled bitstrings) when measuring a random quantum circuit provides a practical benchmark for the quality of a quantum computer and a quantitative noise characterization method. We analytically estimate the difference in the expected number of collisions when sampling bitstrings from a pure random state and when sampling from the classical uniform distribution. We show that this quantity, if properly normalized, can be used as a "collision anomaly" benchmark or as a "collision volume" test which is similar to the well-known quantum volume test, with advantages (no classical computing cost) and disadvantages (high sampling cost). We also propose to count the number of cross-collisions between two independent quantum computers running the same random circuit in order to obtain a cross-validation test of the two devices. Finally, we quantify the sampling cost of quantum collision experiments. We find that the sampling cost for running a collision volume test on state-of-the-art processors (e.g.~20 effective clean qubits) is quite small: less than $10^5$ shots. For large-scale experiments in the quantum supremacy regime the required number of shots for observing a quantum signal in the observed number of collisions is currently infeasible ($>10^{12}$), but not completely out of reach for near-future technology.

quant-ph↗

arXiv2023

Exact and approximate simulation of large quantum circuits on a single GPU

We benchmark the performances of Qrack, an open-source software library for the high-performance classical simulation of (gate-model) quantum computers. Qrack simulates, in the Schrödinger picture, the exact quantum state of $n$ qubits evolving under the application of a circuit composed of elementary quantum gates. Moreover, Qrack can also run approximate simulations in which a tunable reduction of the quantum state fidelity is traded for a significant reduction of the execution time and memory footprint. In this work, we give an overview of both simulation methods (exact and approximate), highlighting the main physics-based and software-based techniques. Moreover, we run computationally heavy benchmarks on a single GPU, executing large quantum Fourier transform circuits and large random circuits. Compared with other classical simulators, we report competitive execution times for the exact simulation of Fourier transform circuits with up to 27 qubits. We also demonstrate the approximate simulation of all amplitudes of random circuits acting on 54 qubits with 7 layers at average fidelity higher than $4\%$, a task commonly considered hard without super-computing resources.

quant-ph↗

arXiv2023

Zero noise extrapolation on logical qubits by scaling the error correction code distance

In this work, we migrate the quantum error mitigation technique of Zero-Noise Extrapolation (ZNE) to fault-tolerant quantum computing. We employ ZNE on logically encoded qubits rather than physical qubits. This approach will be useful in a regime where quantum error correction (QEC) is implementable but the number of qubits available for QEC is limited. Apart from illustrating the utility of a traditional ZNE approach (circuit-level unitary folding) for the QEC regime, we propose a novel noise scaling ZNE method specifically tailored to QEC: distance scaled ZNE (DS-ZNE). DS-ZNE scales the distance of the error correction code, and thereby the resulting logical error rate, and utilizes this code distance as the scaling `knob' for ZNE. Logical qubit error rates are scaled until the maximum achievable code distance for a fixed number of physical qubits, and lower error rates (i.e., effectively higher code distances) are achieved via extrapolation techniques migrated from traditional ZNE. Furthermore, to maximize physical qubit utilization over the ZNE experiments, logical executions at code distances lower than the maximum allowed by the physical qubits on the quantum device are parallelized to optimize device utilization. We validate our proposal with numerical simulation and confirm that ZNE lowers the logical error rates and increases the effective code distance beyond the physical capability of the quantum device. For instance, at a physical code distance of 11, the DS-ZNE effective code distance is 17, and at a physical code distance of 13, the DS-ZNE effective code distance is 21. When the proposed technique is compared against unitary folding ZNE under the constraint of a fixed number of executions of the quantum device, DS-ZNE outperforms unitary folding by up to 92% in terms of the post-ZNE logical error rate.

quant-ph↗

arXiv2023

Increasing the Measured Effective Quantum Volume with Zero Noise Extrapolation

Quantum Volume is a full-stack benchmark for near-term quantum computers. It quantifies the largest size of a square circuit which can be executed on the target device with reasonable fidelity. Error mitigation is a set of techniques intended to remove the effects of noise present in the computation of noisy quantum computers when computing an expectation value of interest. Effective quantum volume is a proposed metric that applies error mitigation to the quantum volume protocol in order to evaluate the effectiveness not only of the target device but also of the error mitigation algorithm. Digital Zero-Noise Extrapolation (ZNE) is an error mitigation technique that estimates the noiseless expectation value using circuit folding to amplify errors by known scale factors and extrapolating to the zero-noise limit. Here we demonstrate that ZNE, with global and local unitary folding with fractional scale factors, in conjunction with dynamical decoupling, can increase the effective quantum volume over the vendor-measured quantum volume. Specifically, we measure the effective quantum volume of four IBM Quantum superconducting processor units, obtaining values that are larger than the vendor-measured quantum volume on each device. This is the first such increase reported.

quant-ph↗

arXiv2022

Testing platform-independent quantum error mitigation on noisy quantum computers

We apply quantum error mitigation techniques to a variety of benchmark problems and quantum computers to evaluate the performance of quantum error mitigation in practice. To do so, we define an empirically motivated, resource-normalized metric of the improvement of error mitigation which we call the improvement factor, and calculate this metric for each experiment we perform. The experiments we perform consist of zero-noise extrapolation and probabilistic error cancellation applied to two benchmark problems run on IBM, IonQ, and Rigetti quantum computers, as well as noisy quantum computer simulators. Our results show that error mitigation is on average more beneficial than no error mitigation - even when normalized by the additional resources used - but also emphasize that the performance of quantum error mitigation depends on the underlying computer.

quant-ph↗

arXiv2022

Automated quantum error mitigation based on probabilistic error reduction

Current quantum computers suffer from a level of noise that prohibits extracting useful results directly from longer computations. The figure of merit in many near-term quantum algorithms is an expectation value measured at the end of the computation, which experiences a bias in the presence of hardware noise. A systematic way to remove such bias is probabilistic error cancellation (PEC). PEC requires a full characterization of the noise and introduces a sampling overhead that increases exponentially with circuit depth, prohibiting high-depth circuits at realistic noise levels. Probabilistic error reduction (PER) is a related quantum error mitigation method that systematically reduces the sampling overhead at the cost of reintroducing bias. In combination with zero-noise extrapolation, PER can yield expectation values with an accuracy comparable to PEC.Noise reduction through PER is broadly applicable to near-term algorithms, and the automated implementation of PER is thus desirable for facilitating its widespread use. To this end, we present an automated quantum error mitigation software framework that includes noise tomography and application of PER to user-specified circuits. We provide a multi-platform Python package that implements a recently developed Pauli noise tomography (PNT) technique for learning a sparse Pauli noise model and exploits a Pauli noise scaling method to carry out PER.We also provide software tools that leverage a previously developed toolchain, employing PyGSTi for gate set tomography and providing a functionality to use the software Mitiq for PER and zero-noise extrapolation to obtain error-mitigated expectation values on a user-defined circuit.

quant-ph↗

arXiv2022

Analyzing the impact of time-correlated noise on zero-noise extrapolation

Zero-noise extrapolation is a quantum error mitigation technique that has typically been studied under the ideal approximation that the noise acting on a quantum device is not time-correlated. In this work, we investigate the feasibility and performance of zero-noise extrapolation in the presence of time-correlated noise. We show that, in contrast to white noise, time-correlated noise is harder to mitigate via zero-noise extrapolation because it is difficult to scale the noise level without also modifying its spectral distribution. This limitation is particularly strong if "local" gate-level methods are applied for noise scaling. However, we find that "global" noise scaling methods, e.g., global unitary folding, can be sufficiently reliable even in the presence of time-correlated noise. We also introduce gate Trotterization as a new noise scaling technique that may be of independent interest.

quant-ph↗

arXiv2022

Mitiq: A software package for error mitigation on noisy quantum computers

We introduce Mitiq, a Python package for error mitigation on noisy quantum computers. Error mitigation techniques can reduce the impact of noise on near-term quantum computers with minimal overhead in quantum resources by relying on a mixture of quantum sampling and classical post-processing techniques. Mitiq is an extensible toolkit of different error mitigation methods, including zero-noise extrapolation, probabilistic error cancellation, and Clifford data regression. The library is designed to be compatible with generic backends and interfaces with different quantum software frameworks. We describe Mitiq using code snippets to demonstrate usage and discuss features and contribution guidelines. We present several examples demonstrating error mitigation on IBM and Rigetti superconducting quantum processors as well as on noisy simulators.

quant-ph↗

arXiv2022

Error mitigation increases the effective quantum volume of quantum computers

Quantum volume is a single-number metric which, loosely speaking, reports the number of usable qubits on a quantum computer. While improvements to the underlying hardware are a direct means of increasing quantum volume, the metric is "full-stack" and has also been increased by improvements to software, notably compilers. We extend this latter direction by demonstrating that error mitigation, a type of indirect compilation, increases the effective quantum volume of several quantum computers. Importantly, this increase occurs while taking the same number of overall samples. We encourage the adoption of quantum volume as a benchmark for assessing the performance of error mitigation techniques.

quant-ph↗

arXiv2021

VAQEM: A Variational Approach to Quantum Error Mitigation

Variational Quantum Algorithms (VQAs) are relatively robust to noise, but errors are still a significant detriment to VQAs on near-term quantum machines. It is imperative to employ error mitigation techniques to improve VQA fidelity. While existing error mitigation techniques built from theory provide substantial gains, the disconnect between theory and real machine execution limits their benefits. Thus, it is critical to optimize mitigation techniques to explicitly suit the target application as well as the noise characteristics of the target machine. We propose VAQEM, which dynamically tailors existing error mitigation techniques to the actual, dynamic noisy execution characteristics of VQAs on a target quantum machine. We do so by tuning specific features of these mitigation techniques similar to the traditional rotation angle parameters - by targeting improvements towards a specific objective function which represents the VQA problem at hand. In this paper, we target two types of error mitigation techniques which are suited to idle times in quantum circuits: single qubit gate scheduling and the insertion of dynamical decoupling sequences. We gain substantial improvements to VQA objective measurements - a mean of over 3x across a variety of VQA applications, run on IBM Quantum machines. More importantly, the proposed variational approach is general and can be extended to many other error mitigation techniques whose specific configurations are hard to select a priori. Integrating more mitigation techniques into the VAQEM framework can lead to potentially realizing practically useful VQA benefits on today's noisy quantum machines.

quant-ph↗

arXiv2021

Extending quantum probabilistic error cancellation by noise scaling

We propose a general framework for quantum error mitigation that combines and generalizes two techniques: probabilistic error cancellation (PEC) and zero-noise extrapolation (ZNE). Similarly to PEC, the proposed method represents ideal operations as linear combinations of noisy operations that are implementable on hardware. However, instead of assuming a fixed level of hardware noise, we extend the set of implementable operations by noise scaling. By construction, this method encompasses both PEC and ZNE as particular cases and allows us to investigate a larger set of hybrid techniques. For example, gate extrapolation can be used to implement PEC without requiring knowledge of the device's noise model, e.g., avoiding gate set tomography. Alternatively, probabilistic error reduction can be used to estimate expectation values at intermediate virtual noise strengths (below the hardware level), obtaining partially mitigated results at a lower sampling cost. Moreover, multiple results obtained with different noise reduction factors can be further post-processed with ZNE to better approximate the zero-noise limit.

quant-ph↗

arXiv2021

Estimating the gradient and higher-order derivatives on quantum hardware

For a large class of variational quantum circuits, we show how arbitrary-order derivatives can be analytically evaluated in terms of simple parameter-shift rules, i.e., by running the same circuit with different shifts of the parameters. As particular cases, we obtain parameter-shift rules for the Hessian of an expectation value and for the metric tensor of a variational state, both of which can be efficiently used to analytically implement second-order optimization algorithms on a quantum computer. We also consider the impact of statistical noise by studying the mean squared error of different derivative estimators. In the second part of this work, some of the theoretical techniques for evaluating quantum derivatives are applied to their typical use case: the implementation of quantum optimizers. We find that the performance of different estimators and optimizers is intertwined with the values of different hyperparameters, such as a step size or a number of shots. Our findings are supported by several numerical and hardware experiments, including an experimental estimation of the Hessian of a simple variational circuit and an implementation of the Newton optimizer.

quant-ph↗

arXiv2021

Digital zero noise extrapolation for quantum error mitigation

Zero-noise extrapolation (ZNE) is an increasingly popular technique for mitigating errors in noisy quantum computations without using additional quantum resources. We review the fundamentals of ZNE and propose several improvements to noise scaling and extrapolation, the two key components in the technique. We introduce unitary folding and parameterized noise scaling. These are digital noise scaling frameworks, i.e. one can apply them using only gate-level access common to most quantum instruction sets. We also study different extrapolation methods, including a new adaptive protocol that uses a statistical inference framework. Benchmarks of our techniques show error reductions of 18X to 24X over non-mitigated circuits and demonstrate ZNE effectiveness at larger qubit numbers than have been tested previously. In addition to presenting new results, this work is a self-contained introduction to the practical use of ZNE by quantum programmers.

quant-ph↗