Quantum circuits for exact unitary $t$-designs and applications to higher-order randomized benchmarking

Nakata, Yoshifumi; Zhao, Da; Okuda, Takayuki; Bannai, Eiichi; Suzuki, Yasunari; Tamiya, Shiro; Heya, Kentaro; Yan, Zhiguang; Zuo, Kun; Tamate, Shuhei; Tabuchi, Yutaka; Nakamura, Yasunobu

doi:10.48550/arxiv.2102.12617

Cited by 4 publications

(5 citation statements)

References 83 publications

(158 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The appearance of quantum state-designs in a physical system has also quantum information science applications, in particular for tasks like state-tomography, benchmarking, or cryptography, which employ ensembles of random unitaries or states [16][17][18][19][20][21][22][23][24][25][26][27][28][29]38]. For example, by applying random unitaries, projectively measuring, and processing the classical data, one can in certain cases reconstruct an approximate description of a system's state in a protocol called classical shadow tomography [26].…”

Section: Theoremmentioning

confidence: 99%

“…of the distribution of projected states over H A . We note that understanding statistical properties of ensembles of quantum states or unitaries (specifically quantifying the degree of randomness) forms the basis of many applications in quantum information science such as cryptography, tomography, or machine learning, as well as sampling-based computational-advantage tests for near-term quantum devices [16][17][18][19][20][21][22][23][24][25][26][27][28][29]. Eq.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Exact emergent quantum state designs from quantum chaotic dynamics

Ho,

Choi

2021

Preprint

View full text Add to dashboard Cite

We present exact results on a novel kind of emergent random matrix universality that quantum many-body systems at infinite temperature can exhibit. Specifically, we consider an ensemble of pure states supported on a small subsystem, generated from projective measurements of the remainder of the system in a local basis. We rigorously show that the ensemble, derived for a class of quantum chaotic systems undergoing quench dynamics, approaches a universal form completely independent of system details: it becomes uniformly distributed in Hilbert space. This goes beyond the standard paradigm of quantum thermalization, which dictates that the subsystem relaxes to an ensemble of quantum states that reproduces the expectation values of local observables in a thermal mixed state. Our results imply more generally that the distribution of quantum states themselves becomes indistinguishable from those of uniformly random ones, i.e. the ensemble forms a quantum state-design in the parlance of quantum information theory. Our work establishes bridges between quantum many-body physics, quantum information and random matrix theory, by showing that pseudo-random states can arise from isolated quantum dynamics, opening up new ways to design applications for quantum state tomography and benchmarking.

show abstract

Section: Theoremmentioning

confidence: 99%

mentioning

confidence: 99%

Exact emergent quantum state designs from quantum chaotic dynamics

Ho,

Choi

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…We constructed basic software for asynchronous control of such devices and automatic and fast calibration of a large number of qubits. We also proposed efficient methods for characterization and Flexible and high-performance measurement systems calibration using machine learning and quantum randomness [2,3]. The second topic is the design of peripheral circuits that execute the operations and feedback required for quantum error correction.…”

Section: Research and Development For Fault-tolerant Quantum Computingmentioning

confidence: 99%

Fault-tolerant Technology for Quantum Information Processing and Its Implementation Methods

Tokunaga¹,

Suzuki²,

Endo³

et al. 2021

NTT Technical Review

View full text Add to dashboard Cite

To use quantum information processing in a wide range of applications, fault-tolerant processing is essential to cope with noise. Fault-tolerant quantum computing using quantum error-correcting codes is scalable, but the overhead of number of qubits or processes is large, so improving efficiency is an important research theme. Quantum error mitigation incurs computational cost, but it does not require the overhead of number of qubits, so it is expected to be used for near-future applications. In this article, we introduce our research activities on these topics as well as our studies toward the implementation of quantum information processing.

show abstract

“…Recent work has sought to deepen the core benchmarking toolkit, for example by considering higherorder moment analysis [21], character benchmarking techniques [22], the extension to benchmarking of logical qubits [23] and analogue regimes [24]. In this work we first consider general structural questions on quantum channels, and then address their relationship to benchmarking scenarios.…”

Section: Introductionmentioning

confidence: 99%

Estimation of correlations and non-separability in quantum channels via unitarity benchmarking

Girling,

Cirstoiu,

Jennings

2021

Preprint

View full text Add to dashboard Cite

The ability to transfer coherent quantum information between systems is a fundamental component of quantum technologies and leads to coherent correlations within the global quantum process. However correlation structures in quantum channels are less studied than those in quantum states. Motivated by recent techniques in randomized benchmarking, we develop a range of results for efficient estimation of correlations within a bipartite quantum channel. We introduce sub-unitarity measures that are invariant under local changes of basis, generalize the unitarity of a channel, and allow for the analysis of coherent information exchange within channels. Using these, we show that unitarity is monogamous, and provide a novel information-disturbance relation. We then define a notion of correlated unitarity that quantifies the correlations within a given channel. Crucially, we show that this measure is strictly bounded on the set of separable channels and therefore provides a witness of non-separability. Finally, we describe how such measures for effective noise channels can be efficiently estimated within different randomized benchmarking protocols. We find that the correlated unitarity can be estimated in a SPAM-robust manner for any separable quantum channel, and show that a benchmarking/tomography protocol with mid-circuit resets can reliably witness nonseparability for sufficiently small reset errors. The tools we develop provide information beyond that obtained via simultaneous randomized benchmarking and so could find application in the analysis of cross-talk and coherent errors in quantum devices.

show abstract

Quantum circuits for exact unitary $t$-designs and applications to higher-order randomized benchmarking

Cited by 4 publications

References 83 publications

Exact emergent quantum state designs from quantum chaotic dynamics

Exact emergent quantum state designs from quantum chaotic dynamics

Fault-tolerant Technology for Quantum Information Processing and Its Implementation Methods

Estimation of correlations and non-separability in quantum channels via unitarity benchmarking

Contact Info

Product

Resources

About