40 Search Results

Midcircuit measurements (MCMs) are crucial ingredients in the development of fault-tolerant quantum computation. While there have been rapid experimental progresses in realizing MCMs, a systematic method for characterizing noisy MCMs is still under exploration. In this work, we develop a cycle benchmarking (CB)-type algorithm to characterize noisy MCMs. The key idea is to use a joint Fourier transform on the classical and quantum registers and then estimate parameters in the Fourier space, analogous to Pauli fidelities used in CB-type algorithms for characterizing the Pauli-noise channel of Clifford gates. Furthermore, we develop a theory of the noise learnability of MCMs, which determines what information can be learned about the noise model (in the presence of state preparation and terminating measurement noise) and what cannot, which shows that all learnable information can be learned using our algorithm. As an application, we show how to use the learned information to test the independence between measurement noise and state-preparation noise in an MCM. Finally, we conduct numerical simulations to illustrate the practical applicability of the algorithm. Similar to other CB-type algorithms, we expect the algorithm to provide a useful toolkit that is of experimental interest. Published by the American Physical Society 2025

The generation of $k$ -designs (pseudorandom distributions that emulate the Haar measure up to $k$ moments) with local quantum circuit ensembles is a problem of fundamental importance in quantum information and physics. Despite the extensive understanding of this problem for ordinary random circuits, the crucial situations in which symmetries or conservation laws are in play are known to pose fundamental challenges and remain little understood. Here, we construct explicit local unitary ensembles that can achieve high-order unitary $k$ -designs under transversal continuous symmetry, in the particularly important $\mathrm{SU}\left(d\right)$ case. Specifically, we define the convolutional quantum alternating (CQA) group generated by 4-local $\mathrm{SU}\left(d\right)$ -symmetric Hamiltonians as well as associated 4-local $\mathrm{SU}\left(d\right)$ -symmetric random unitary circuit ensembles and prove that they form and converge to $\mathrm{SU}\left(d\right)$ -symmetric $k$ -designs, respectively, for all $k<n(n-3)/2$ , with $n$ being the number of qudits. A key technique that we employ to obtain the results is the Okounkov-Vershik approach to $S_n$ representation theory. To study the convergence time of the CQA ensemble, we develop a numerical method using the Young orthogonal form and the $S_n$ branching rule. We provide strong evidence for a subconstant spectral gap and certain convergence time scales of various important circuit architectures, which contrast with the symmetry-free case. We also provide comprehensive explanations of the difficulties and limitations in rigorously analyzing the convergence time using methods that have been effective for cases without symmetries, including Knabe’s local gap threshold and Nachtergaele’s martingale methods. This suggests that a novel approach is likely necessary for understanding the convergence time of $\mathrm{SU}\left(d\right)$ -symmetric local random circuits. Published by the American Physical Society 2024

Entanglement is an extraordinary feature of quantum mechanics. Sources of entangled optical photons were essential to test the foundations of quantum physics through violations of Bell’s inequalities. More recently, entangled many-body states have been realized via strong nonlinear interactions in microwave circuits with superconducting qubits. Here, we demonstrate a chip-scale source of entangled optical and microwave photonic qubits. Our device platform integrates a piezo-optomechanical transducer with a superconducting resonator which is robust under optical illumination. We drive a photon-pair generation process and employ a dual-rail encoding intrinsic to our system to prepare entangled states of microwave and optical photons. We place a lower bound on the fidelity of the entangled state by measuring microwave and optical photons in two orthogonal bases. This entanglement source can directly interface telecom wavelength time-bin qubits and gigahertz frequency superconducting qubits, two well-established platforms for quantum communication and computation, respectively. Published by the American Physical Society 2024

Fault-tolerant quantum computation with bosonic qubits often necessitates the use of noisy discrete-variable ancillae. In this work, we establish a comprehensive and practical fault-tolerance framework for such a hybrid system and synthesize it with fault-tolerant protocols by combining bosonic quantum error correction (QEC) and advanced quantum control techniques. We introduce essential building blocks of error-corrected gadgets by leveraging ancilla-assisted bosonic operations using a generalized variant of path-independent quantum control. Using these building blocks, we construct a universal set of error-corrected gadgets that tolerate a single-photon loss and an arbitrary ancilla fault for four-legged cat qubits. Notably, our construction requires only dispersive coupling between bosonic modes and ancillae, as well as beam-splitter coupling between bosonic modes, both of which have been experimentally demonstrated with strong strengths and high accuracy. Moreover, each error-corrected bosonic qubit is comprised of only a single bosonic mode and a three-level ancilla, featuring the hardware efficiency of bosonic QEC in the full fault-tolerant setting. We numerically demonstrate the feasibility of our schemes using current experimental parameters in the circuit-QED platform. Finally, we present a hardware-efficient architecture for fault-tolerant quantum computing by concatenating the four-legged cat qubits with an outer qubit code utilizing only beam-splitter couplings. Our estimates suggest that the overall noise threshold can be reached using existing hardware. These developed fault-tolerant schemes extend beyond their applicability to four-legged cat qubits and can be adapted for other rotation-symmetrical codes, offering a promising avenue toward scalable and robust quantum computation with bosonic qubits. Published by the American Physical Society 2024

Abstract Large machine learning models are revolutionary technologies of artificial intelligence whose bottlenecks include huge computational expenses, power, and time used both in the pre-training and fine-tuning process. In this work, we show that fault-tolerant quantum computing could possibly provide provably efficient resolutions for generic (stochastic) gradient descent algorithms, scaling as$$$${{{{{{{\mathcal{O}}}}}}}}({T}^{2}\times {{{{{{{\rm{polylog}}}}}}}}(n))$$$$ $O\left(T^2\times \mathrm{polylog}\left(n\right)\right)$, wherenis the size of the models andTis the number of iterations in the training, as long as the models are both sufficiently dissipative and sparse, with small learning rates. Based on earlier efficient quantum algorithms for dissipative differential equations, we find and prove that similar algorithms work for (stochastic) gradient descent, the primary algorithm for machine learning. In practice, we benchmark instances of large machine learning models from 7 million to 103 million parameters. We find that, in the context of sparse training, a quantum enhancement is possible at the early stage of learning after model pruning, motivating a sparse parameter download and re-upload scheme. Our work shows solidly that fault-tolerant quantum algorithms could potentially contribute to most state-of-the-art, large-scale machine-learning problems.

Cross-entropy (XE) measure is a widely used benchmark to demonstrate quantum computational advantage from sampling problems, such as random circuit sampling using superconducting qubits and boson sampling (BS). We present a heuristic classical algorithm that attains a better XE than the current BS experiments in a verifiable regime and is likely to attain a better XE score than the near-future BS experiments in a reasonable running time. The key idea behind the algorithm is that there exist distributions that correlate with the ideal BS probability distribution and that can be efficiently computed. The correlation and the computability of the distribution enable us to postselect heavy outcomes of the ideal probability distribution without computing the ideal probability, which essentially leads to a large XE. Our method scores a better XE than the recent Gaussian BS experiments when implemented at intermediate, verifiable system sizes. Much like current state-of-the-art experiments, we cannot verify that our spoofer works for quantum-advantage-size systems. However, we demonstrate that our approach works for much larger system sizes in fermion sampling, where we can efficiently compute output probabilities. Finally, we provide analytic evidence that the classical algorithm is likely to spoof noisy BS efficiently.

We propose an autonomous quantum error correction scheme using squeezed cat (SC) code against excitation loss in continuous-variable systems. Through reservoir engineering, we show that a structured dissipation can stabilize a two-component SC while autonomously correcting the errors. The implementation of such dissipation only requires low-order nonlinear couplings among three bosonic modes or between a bosonic mode and a qutrit. While our proposed scheme is device independent, it is readily implementable with current experimental platforms such as superconducting circuits and trapped-ion systems. Compared to the stabilized cat, the stabilized SC has a much lower dominant error rate and a significantly enhanced noise bias. Furthermore, the bias-preserving operations for the SC have much lower error rates. In combination, the stabilized SC leads to substantially better logical performance when concatenating with an outer discrete-variable code. The surface-SC scheme achieves more than one order of magnitude increase in the threshold ratio between the loss rate κ₁ and the engineered dissipation rate κ₂. Under a practical noise ratio κ₁/κ₂ = 10^-3, the repetition-SC scheme can reach a 10^-15 logical error rate even with a small mean excitation number of 4, which already suffices for practically useful quantum algorithms.

Fault-tolerant quantum computation with depolarization error often requires demanding error threshold and resource overhead. If the operations can maintain high noise bias—dominated by dephasing error with small bit-flip error—we can achieve hardware-efficient fault-tolerant quantum computation with a more favorable error threshold. Distinct from two-level physical systems, multilevel systems (such as harmonic oscillators) can achieve a desirable set of bias-preserving quantum operations while using continuous engineered dissipation or Hamiltonian protection to stabilize to the encoding subspace. For example, cat codes stabilized with driven-dissipation or Kerr nonlinearity can possess a set of bias-preserving gates while continuously correcting bosonic dephasing error. However, cat codes are not compatible with continuous quantum error correction against excitation loss error, because it is challenging to continuously monitor the parity to correct photon loss errors. In this work, we generalize the bias-preserving operations to pair-cat codes, which can be regarded as a multimode generalization of cat codes, to be compatible with continuous quantum error correction against both bosonic loss and dephasing errors. In conclusion, our results open the door towards hardware-efficient robust quantum information processing with both bias-preserving operations and continuous quantum error correction simultaneously correcting bosonic loss and dephasing errors.

Mitigating errors in quantum information processing devices is especially important in the absence of fault tolerance. An effective method in suppressing state-preparation errors is using multiple copies to distill the ideal component from a noisy quantum state. Here, we use classical shadows and randomized measurements to circumvent the need for coherent access to multiple copies at an exponential cost. We study the scaling of resources using numerical simulations and find that the overhead is still favorable compared to full state tomography. We optimize measurement resources under realistic experimental constraints and apply our method to an experiment preparing a Greenberger-Horne-Zeilinger state with trapped ions. In addition to improving stabilizer measurements, the analysis of the improved results reveals the nature of errors affecting the experiment. Hence, our results provide a directly applicable method for mitigating errors in near-term quantum computers.

Recently, several quantum benchmarking algorithms have been developed to characterize noisy quantum gates on today’s quantum devices. A fundamental issue in benchmarking is that not everything about quantum noise is learnable due to the existence of gauge freedom, leaving open the question what information is learnable and what is not, which is unclear even for a single CNOT gate. Here we give a precise characterization of the learnability of Pauli noise channels attached to Clifford gates using graph theoretical tools. Our results reveal the optimality of cycle benchmarking in the sense that it can extract all learnable information about Pauli noise. We experimentally demonstrate noise characterization of IBM’s CNOT gate up to 2 unlearnable degrees of freedom, for which we obtain bounds using physical constraints. In addition, we show that an attempt to extract unlearnable information by ignoring state preparation noise yields unphysical estimates, which is used to lower bound the state preparation noise.