Eigenstate thermalization in dual-unitary quantum circuits: Asymptotics of spectral functions

Fritzsch, Felix; Prosen, Tomaž

doi:10.1103/physreve.103.062133

Cited by 32 publications

(15 citation statements)

References 86 publications

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“…[23], within dual-unitary circuit models the only nontrivial correlations are those on the edge of the light cone, which can be exactly calculated using a quantum channel approach. Dual-unitary models have since been the subject of intensive study [14,[24][25][26][27][28][29][30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Correlations and commuting transfer matrices in integrable unitary circuits

2022

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We consider a unitary circuit where the underlying gates are chosen to be \check{R}Ř-matrices satisfying the Yang-Baxter equation and correlation functions can be expressed through a transfer matrix formalism. These transfer matrices are no longer Hermitian and differ from the ones guaranteeing local conservation laws, but remain mutually commuting at different values of the spectral parameter defining the circuit. Exact eigenstates can still be constructed as a Bethe ansatz, but while these transfer matrices are diagonalizable in the inhomogeneous case, the homogeneous limit corresponds to an exceptional point where multiple eigenstates coalesce and Jordan blocks appear. Remarkably, the complete set of (generalized) eigenstates is only obtained when taking into account a combinatorial number of nontrivial vacuum states. In all cases, the Bethe equations reduce to those of the integrable spin-1 chain and exhibit a global SU(2) symmetry, significantly reducing the total number of eigenstates required in the calculation of correlation functions. A similar construction is shown to hold for the calculation of out-of-time-order correlations.

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Section: Introductionmentioning

confidence: 99%

Correlations and commuting transfer matrices in integrable unitary circuits

2022

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“…Random quantum circuits, due to their finetuned structure, allow exact analysis of the spectral statistics, which sheds light on the underlying mechanism responsible for the emergence of RMT structure. In addition to the RMT spectral statistics, random quantum circuits also exhibit other fundamental properties of many-body quantum chaotic systems, such as the decay of correlation functions of local observables [35,36], ballistic spreading of the local operators [13,[37][38][39][40][41][42][43], ballistic growth of the entanglement [13,36,37,[44][45][46][47][48], and Gaussian distribution of the matrix elements of observables in the energy eigenbasis (as expected from the eigenstate thermalization hypothesis [49][50][51]) [52,53]. Experimentally, random quantum circuits can been simulated in the noisy intermediate-scale quantum (NISQ) devices [54] built with superconducting qudits [55,56], trapped ions [57,58], and Rydberg atoms [59], and some of these generic features for quantum chaotic systems have been observed [60].…”

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confidence: 99%

Effective field theory of random quantum circuits

Liao,

Galitski

2022

Preprint

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Quantum circuits have been widely used as a platform to simulate generic quantum many-body systems. In particular, random quantum circuits provide a means to probe universal features of many-body quantum chaos and ergodicity. Some such features have already been experimentally demonstrated in the noisy intermediate-scale quantum (NISQ) devices. On the theory side, properties of random quantum circuits have been studied on a case-by-case basis and for certain specific systems, a hallmark of quantum chaos -universal Wigner-Dyson level statistics -has been derived. This work develops an effective field theory for a large class of random quantum circuits. The theory has the form of a replica sigma model and is similar to the low-energy approach to diffusion in disordered systems. The method is used to explicitly derive universal random matrix behavior of a large family of random circuits. In particular, we rederive Wigner-Dyson spectral statistics of the brickwork circuit model by Chan, De Luca, and Chalker [Phys. Rev. X 8, 041019 (2018)] and show within the same calculation that its various permutations and higher-dimensional generalizations preserve the universal level statistics. Finally, we use the replica sigma model framework to rederive the Weingarten calculus, which is a method to evaluate integrals of polynomials of matrix elements with respect to the Haar measure over compact groups and has many applications in the studies of quantum circuits. The effective field theory, derived here, provides both a method to quantitatively characterize quantum dynamics of random Floquet systems (e.g., calculating operator and entanglement spreading) and also path to understanding the general fundamental mechanism behind quantum chaos and thermalization in these systems.

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“…Secondly, it can be easily shown that an arbitrary product of single-qubit gates can be implemented by substituting suitable u 1 ⊗ u 2 • SWAP gates for some of SWAP gates in Eqs. (35) and (36). A quantum circuit consisting of arbitrary one-qubit gates and CZ gates has capability to efficiently simulate arbitrary quantum circuit consisting of poly(n) nearest-neighbor two-qubit gates [41].…”

Section: D Duqc Is Universal In Late Timementioning

confidence: 99%

Computational power of one- and two-dimensional dual-unitary quantum circuits

Suzuki

Mitarai

Fujii

2022

Quantum

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Quantum circuits that are classically simulatable tell us when quantum computation becomes less powerful than or equivalent to classical computation. Such classically simulatable circuits are of importance because they illustrate what makes universal quantum computation different from classical computers. In this work, we propose a novel family of classically simulatable circuits by making use of dual-unitary quantum circuits (DUQCs), which have been recently investigated as exactly solvable models of non-equilibrium physics, and we characterize their computational power. Specifically, we investigate the computational complexity of the problem of calculating local expectation values and the sampling problem of one-dimensional DUQCs, and we generalize them to two spatial dimensions. We reveal that a local expectation value of a DUQC is classically simulatable at an early time, which is linear in a system length. In contrast, in a late time, they can perform universal quantum computation, and the problem becomes a BQP-complete problem. Moreover, classical simulation of sampling from a DUQC turns out to be hard.

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Eigenstate thermalization in dual-unitary quantum circuits: Asymptotics of spectral functions

Cited by 32 publications

References 86 publications

Correlations and commuting transfer matrices in integrable unitary circuits

Correlations and commuting transfer matrices in integrable unitary circuits

Effective field theory of random quantum circuits

Computational power of one- and two-dimensional dual-unitary quantum circuits

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