Dec 2024· Quantum Science and Technology· Vol 11, pp. 035052· 4 citations
Physics
TL;DR
This work introduces a broad framework for enhancing the sample efficiency of RB that is sufficiently powerful to extend the practical reach of RB beyond the multiqubit setting, and shows that synthetic RB protocols can reduce the complexity of measuring rotationally invariant error rates by two orders of magnitude relative to standard approaches.
Abstract
Noise characterization methods such as randomized benchmarking (RB) are critical for the development of scalable quantum computers. Modern RB protocols for multiqubit systems extract physically relevant error rates by exploiting the structure of the group representation generated by the set of benchmarked operations. However, existing techniques become prohibitively inefficient for representations that are highly reducible yet decompose into irreducible subspaces of high dimension. These situations prevail when benchmarking high-dimensional systems such as qudits or bosonic modes, where experimental control is limited to implementing a small subset of all possible unitary operations. We introduce a broad framework for enhancing the sample efficiency of RB that is sufficiently powerful to extend the practical reach of RB beyond the multiqubit setting. Our strategy, which applies to any benchmarking group, uses ‘synthetic’ quantum circuits with classical post-processing of both input and output data to leverage the full structure of reducible superoperator representations. To demonstrate the efficacy of our approach, we develop a detailed theory of RB for systems with rotational symmetry. Such systems carry a natural action of the group SU(2), and they form the basis for several novel quantum error-correcting codes. We show that, for experimentally accessible high-spin systems, synthetic RB protocols can reduce the complexity of measuring rotationally invariant error rates by two orders of magnitude relative to standard approaches such as character RB.
Multipartite Bell tests provide a correlation-only route to benchmarking quantum processors, but their application at large scales is hindered by the rapid decay of many-body correlators under noise and exponentially many terms in conventional Bell expressions. Here we address these scalability obstacles by introducing a finite-setting generalized Mermin family of state-tailored Bell inequalities with analytic certification bounds, in which the measurement-setting number $m$ provides an additional certification dimension complementary to the system size $n$. We show that, for the powers-of-two setting choices considered here, increasing $m$ leaves the ideal normalized multipartite quantum value unchanged while lowering the relevant classical bounds, thereby strengthening the Bell-violation ratios and yielding an improved noise-robustness scaling compared to the standard Mermin inequality. We test this construction experimentally on a programmable superconducting processor by preparing Greenberger-Horne-Zeilinger (GHZ) states of up to 80 qubits. Using randomized sampling for direct Bell-operator estimation, we observe Bell ratios that grow exponentially with system size, certify a nonlocality depth of 14, and show that increasing $m$ strengthens both the Bell ratio and depth certification. All results are obtained solely from measured correlators and analytical bounds, without readout correction, tomography, or model-based mitigation. Generalized Mermin inequalities therefore provide a sharper Bell benchmark for noisy large-scale GHZ states.
Jianbin Cai, Jun-Xiang Huang, F. Otto et al.· 0 citations
Quantum benchmarks provide compact measures of performance that are important for evaluating and comparing quantum systems. Circuit-level benchmarks are particularly valuable because they capture the accumulated effects of noise across interacting operations, but existing approaches may require structured gate sets and costly compilation, classical simulation of reference outputs, or subsystem decompositions that do not capture full-register behavior. We introduce Error Per Circuit Layer (EPCL), an overlap-based circuit-level benchmark that estimates an effective layer polarization by applying identical random circuits to two disjoint quantum registers and measuring the overlap between their output states as a function of circuit depth. EPCL avoids classical simulation of ideal output distributions and recovery to a known reference state, and is compatible with arbitrary gate sets, including non-Clifford gates. We derive the expected overlap decay under an ensemble-averaged depolarizing model and identify the assumptions under which the fitted decay parameter represents an effective layer polarization. Numerical simulations show that EPCL recovers the predicted polarization under weak local stochastic noise and remains well described by a single-exponential decay at stronger stochastic noise levels. The simulations further show that coherent errors associated with fixed entangling layers may require Pauli twirling or randomized compiling to produce the expected decay, while inter-register correlations contribute an additional covariance term to the measured overlap. Finally, experiments on IBM quantum hardware demonstrate clear EPCL decay in 8- and 16-qubit implementations. These results support EPCL as a method for measuring aggregate register performance without requiring classical simulation of ideal circuit outputs or restriction to structured gate sets.
Travis Hurant, A. Vezvaee, Swarnadeep Majumder et al.· 0 citations
This thesis studies exact, deterministic preparation of arbitrary dense n-qubit states, the data-loading step in quantum signal and image processing. It derives two syntheses built on the Digital Signal-induced Heap Transform (DsiHT): the QsiHT Fast Path Real Synthesis and the QsiHT Fast Path Complex Synthesis. Both are benchmarked against ten configurations spanning the UCR, isometry, multiplexor, Schmidt/SVD, QSD, and heap-transform families. Several of those are realizations through Qiskit builders or compiler optimization, not from-scratch reimplementations. The n=3 noisy comparison spans ibm_fez, ibm_kingston, and ibm_marrakesh, three 156-qubit IBM Heron r2 processors, where single-submission nine-method jobs permit within-session family-wide Benjamini-Hochberg-corrected comparisons. The frontier-versus-QSD separation reproduces within one calibration on every device, but the within-frontier order does not reproduce across devices or calibration days. A deep-circuit n=8 run on ibm_fez shows the executed-count ordering re-emerge outside the run-to-run spread on the complex target. Depth was not isolated from mapping, gate composition, calibration, or session effects. All methods are exact to machine precision and differ only in cost. Under noise the coarse error tier tracks the executed (routed) two-qubit count, separating the Theta(2^n) frontier from QSD's Theta(4^n) and nothing finer. Both syntheses realize the deployed Qiskit StatePreparation floor of 2^n-n-1 CNOTs, undercutting every other from-scratch method on the as-built CNOT axis. The Real Synthesis serves real (sign-bearing) targets and holds the lowest classical build cost among the exact loaders at large register sizes, through one fast Walsh-Hadamard pass. The Complex Synthesis serves arbitrary complex targets and ties Qiskit's StatePreparation for the lowest simulated sampled error.
A key task in many quantum-computing applications, e.g., quantum simulation and quantum state tomography (QST), is to partition an arbitrary set of operators into mutually commuting subsets for efficient measurements. However, brute-force approaches to this task quickly become intractable as the number and dimensionality of operators grow. Here, we reformulate operator partitioning as a graph-coloring (GC) problem and develop an efficient computational framework to solve it, balancing accuracy and efficiency. Our framework enables leveraging a range of GC algorithms, which we benchmark for operator partitioning. Then, we demonstrate their utility in optimizing QST experiments, where determining non-overlapping data acquisition settings for QST is a major challenge, and prioritizing among these settings, i.e., selecting the experiments that provide the most information. We further show how to perform these experiments by synthesizing Clifford circuits for joint measurement of commuting Pauli operators in multi-qubit systems. We validate our framework across multi-qubit (up to five qubits), multi-qutrit (up to three qutrits), and hybrid qubit-qutrit systems. Our results show that heuristic GC methods substantially reduce the number of required measurement settings for QST and enable priority-based scheduling that maximizes the information gain per experiment. The optimization converges within minutes on a student-grade laptop, providing speedups of several orders of magnitude over brute-force methods already for these relatively small quantum systems. This demonstrates the potential of GC heuristics as a scalable and practical tool for characterization of noisy intermediate-scale quantum devices. We have made the Python implementation of our GC framework to optimize and schedule QST experiments publicly available at https://github.com/ssm8015/QST_GT.git.
Sumukh S. Moudghalya, A. F. Kockum, Akshay Gaikwad· 0 citations
Simulating quantum error correction (QEC) circuits including non-Clifford gates at scale is important to accelerate progress toward fault-tolerant quantum computing. Here we demonstrate that matrix product state (MPS) techniques can handle many QEC circuits exactly and without restriction on gate types. Crucially, we find that MPS efficiency depends sensitively on implementation choices, and we introduce a series of targeted optimizations that reduce bond dimensions and simulation time by several orders of magnitude compared to naive approaches. We illustrate this with examples including: (a) a rotated surface code quantum memory up to distance 11, (b) logical Bell-state preparation up to distance 9, (c) a 15-to-1 magic-state distillation circuit including hundreds of QEC rounds that we optimize to be simulated with only 11 logical qubits (187 physical qubits) and a maximal bond dimension of 64 in under 40 seconds, and (d) a narrow, deep random circuit that scales linearly with the number of T gates. These results demonstrate the importance of circuit-level optimizations and position MPS as a valuable complement to near-Clifford simulators for QEC circuits.
A. Orioli, Chen Zhao, G. Masella et al.· 1 citation
Motivated by recent breakthroughs in the development of spin-based quantum processing units based on exchange-only (EO) spin qubits, we provide a roadmap for the implementation of quantum algorithms on the EO platform, ranging from the NISQ to the fault-tolerant era. To provide an algorithm-driven perspective on the scaling of quantum chips, we consider a range of applications targeting different stages of hardware maturity and formulate requirements for a successful realization. We show that the compilation method Parity Twine perfectly complements the hardware's capabilities to perform tasks such as the quantum Fourier transform or QAOA. Furthermore, we describe an error detection technique native to Parity Twine, which EO qubits can leverage in a unique and advantageous way to improve algorithm performance. Finally, since both near-term algorithmic benchmarks and a long-term perspective can be found in digital quantum simulation, we specifically discuss the fermionic fast Fourier transform and the simulation of Fermi-Hubbard models. The latter is explicitly discussed in the context of quantum error correction and a partially fault-tolerant realization. By providing detailed resource estimates and identifying scaling bottlenecks on each level, our work offers a quantitative perspective on EO-based quantum computing and will inform future hardware design choices.
F. Lohof, Florian Ginzel, Wolfgang Lechner· 0 citations
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