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Quantum Information Processing

Toward a benchmark for quantum computers based on an iterated post-selective protocol

Adrián Ortega, Orsolya Kálmán, Tamás Kiss

Published Aug 7, 2026• 0 citations
Publisher

Abstract

Abstract Applying post selection in each step of an iterated protocol leads to sensitive quantum dynamics that may be utilized to test and benchmark current quantum computers. An example of this type of protocols was originally proposed for the task of matching an unknown quantum state to a reference state. We propose to employ the quantum state matching protocol for the purpose of testing and benchmarking quantum computers. In particular, we implement this scheme on freely available IBM superconducting quantum computers. By comparing measured values with the theoretical conditional probability of the single, final post-selected qubit, which is easy to calculate classically, we define a benchmark metric. Additionally, the standard deviation of the experimental results from their average serves as a secondary benchmark metric, characterizing fluctuations in the given device. A peculiar feature of the considered protocol is that there is a phase parameter of the initially prepared state, on which the resulting conditional probability should not depend. A careful analysis of the measured values indicates that its dependence on the initial phase can reveal useful information about coherent gate errors of the quantum device.

DOI
10.1007/s11128-026-05294-y

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Abstract Applying post selection in each step of an iterated protocol leads to sensitive quantum dynamics that may be utilized to test and benchmark current quantum computers. An example of this type of protocols was originally proposed for the task of matching an unknown quantum state to a reference state. We propose to employ the quantum state matching protocol for the purpose of testing and benchmarking quantum computers. In particular, we implement this scheme on freely available IBM superconducting quantum computers. By comparing measured values with the theoretical conditional probability of the single, final post-selected qubit, which is easy to calculate classically, we define a benchmark metric. Additionally, the standard deviation of the experimental results from their average serves as a secondary benchmark metric, characterizing fluctuations in the given device. A peculiar feature of the considered protocol is that there is a phase parameter of the initially prepared state, on which the resulting conditional probability should not depend. A careful analysis of the measured values indicates that its dependence on the initial phase can reveal useful information about coherent gate errors of the quantum device.
Applying post selection in each step of an iterated protocol leads to sensitive quantum dynamics that may be utilized to test and benchmark current quantum computers. An example of this type of protocols was originally proposed for the task of matching an unknown quantum state to a reference state. We propose to employ the quantum state matching protocol for the purpose of testing and benchmarking quantum computers. In particular, we implement this scheme on freely available IBM superconducting quantum computers. By comparing measured values with the theoretical conditional probability of the single, final post-selected qubit, which is easy to calculate classically, we define a benchmark metric. Additionally, the standard deviation of the experimental results from their average serves as a secondary benchmark metric, characterizing fluctuations in the given device. A peculiar feature of the considered protocol is that there is a phase parameter of the initially prepared state, on which the resulting conditional probability should not depend. A careful analysis of the measured values indicates that its dependence on the initial phase can reveal useful information about coherent gate errors of the quantum device.
Abstract The presence of noise in quantum computers hinders their effective operation. Even though quantum error correction can theoretically remedy this problem, its practical realization is still a challenge. Testing and benchmarking noisy, intermediate-scale quantum (NISC) computers is therefore of high importance. Here, we suggest the application of the so-called quantum state matching protocol for testing purposes. This protocol was originally proposed to determine if an unknown quantum state falls in a prescribed neighborhood of a reference state. We decompose the unitary specific to the protocol and construct the quantum circuit implementing one step of the dynamics for different characteristic parameters of the scheme and present test results for two different IBM quantum computers. By comparing the experimentally obtained relative frequencies of success to the ideal success probability with a maximum statistical tolerance, we discriminate statistical errors from device specific ones. For the characterization of noise, we also use the fact that while the output of the ideal protocol is insensitive to the internal phase of the input state, the actual implementation may lead to deviations. For systematically varied inputs we find that the device with the smaller quantum volume performs better on our tests than the one with larger quantum volume, while for random inputs they show a more similar performance.
The characterization of noisy quantum circuits is an important step in the development of large-scale quantum computers. As experimental quantum architectures approach the threshold for fault-tolerant quantum computing, obtaining a benchmark of process fidelities is needed to verify the integrity of the system and ensure functionality. Additionally, the ability to successfully implement a quantum code of choice may depend on the type of noise that is present in the system. It is therefore necessary to characterize not only the fidelity of the process, but also the structure of the noise. \n \nRandomized benchmarking is a characterization protocol which extracts partial information from a noisy quantum process. This thesis gives a detailed review of the randomized benchmarking protocol, and presents the results of three collaborative projects which use techniques similar to randomized benchmarking to obtain previously hidden information. The first protocol is designed to obtain a benchmark on loss errors. This protocol also provides information on the detector efficiency and an additional constraint on estimated parameters from randomized benchmarking. The second protocol is an extension of the first, under the special case of coherent leakage errors, for which we obtain an estimate of the leakage rate. The third protocol provides a method of testing for spatial correlations in noisy processes. This test may be used to determine the correlation structure of errors, and the error correcting codes needed for successful experiments in a particular architecture. All protocols presented in this thesis are scalable, platform-independent and insensitive to state preparation and measurement errors. We also provide results of numerical tests of these protocols for simulated noise, which show their accuracy and robustness.
Abstract Quantum computers have the potential to outperform classical computers in a range of computational tasks, such as prime factorisation and unstructured searching. However, real-world quantum computers are subject to noise. Quantifying noise is of vital importance, since it is often the dominant factor preventing the successful realisation of advanced quantum computations. Here we propose and demonstrate an interleaved randomised benchmarking protocol for measurement-based quantum computers that can be used to estimate the fidelity of any single-qubit measurement-based gate. We tested the protocol on IBM superconducting quantum processors by estimating the fidelity of the Hadamard and T gates—a universal single-qubit gate set. Measurements were performed on entangled cluster states of up to 31 qubits. Our estimated gate fidelities show good agreement with those calculated from quantum process tomography. By artificially increasing noise, we were able to show that our protocol detects large noise variations in different implementations of a gate.
We present a benchmarking protocol for universal quantum computers, achieved through the simulation of random dynamical quantum maps. This protocol provides a holistic assessment of system-wide error rates, encapsulating both gate inaccuracies and the errors associated with mid-circuit qubit measurements and resets. By employing random quantum circuits and segmenting mid-circuit qubit measurement and reset in a repeated fashion, we steer the system of qubits to an ensemble of steady-states. These steady-states are described by random Wishart matrices, and align with the steady-state characteristics previously identified in random Lindbladian dynamics, including the universality property. The protocol assesses the resulting ensemble probability distribution measured in the computational basis, effectively avoiding a tomographic reconstruction. Our various numerical simulations demonstrate the relationship between the final distribution and different error sources. Additionally, we implement the protocol on state-of-the-art transmon qubits provided by IBM Quantum, drawing comparisons between empirical results, theoretical expectations, and simulations derived from a fitted noise model of the device.
We describe a scalable experimental protocol for estimating the average error of individual quantum computational gates. This protocol consists of interleaving random Clifford gates between the gate of interest and provides an estimate as well as theoretical bounds for the average error of the gate under test, so long as the average noise variation over all Clifford gates is small. This technique takes into account both state preparation and measurement errors and is scalable in the number of qubits. We apply this protocol to a superconducting qubit system and find a bounded average error of 0.003 [0,0.016] for the single-qubit gates X(π/2) and Y(π/2). These bounded values provide better estimates of the average error than those extracted via quantum process tomography.