Exact spectral gaps of random one-dimensional quantum circuits
- URL: http://arxiv.org/abs/2408.11201v1
- Date: Tue, 20 Aug 2024 21:23:42 GMT
- Title: Exact spectral gaps of random one-dimensional quantum circuits
- Authors: Andrew E. Deneris, Pablo Bermejo, Paolo Braccia, Lukasz Cincio, M. Cerezo,
- Abstract summary: spectral gap of local random quantum circuits is a fundamental property that determines how close the moments of the circuit's unitaries match those of a Haar random distribution.
We show that one can exactly compute the associated spectral gaps.
We verify our results by numerically computing the spectral gap for systems of up to 70 qubits, as well as comparing them to gaps of random and symplectic circuits.
- Score: 0.3774866290142281
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The spectral gap of local random quantum circuits is a fundamental property that determines how close the moments of the circuit's unitaries match those of a Haar random distribution. When studying spectral gaps, it is common to bound these quantities using tools from statistical mechanics or via quantum information-based inequalities. By focusing on the second moment of one-dimensional unitary circuits where nearest neighboring gates act on sets of qudits (with open and closed boundary conditions), we show that one can exactly compute the associated spectral gaps. Indeed, having access to their functional form allows us to prove several important results, such as the fact that the spectral gap for closed boundary condition is exactly the square of the gap for open boundaries, as well as improve on previously known bounds for approximate design convergence. Finally, we verify our theoretical results by numerically computing the spectral gap for systems of up to 70 qubits, as well as comparing them to gaps of random orthogonal and symplectic circuits.
Related papers
- Conditional t-independent spectral gap for random quantum circuits and implications for t-design depths [0.0]
We establish a new bound on the spectral gap of the t-th moment of a one-dimensional brickwork architecture on N qudits.
The improved spectral gaps gives large improvements to the constant factors in known results.
arXiv Detail & Related papers (2024-11-20T22:46:10Z) - Quantum advantage from measurement-induced entanglement in random shallow circuits [0.18749305679160366]
We show that long-range measurement-induced entanglement (MIE) proliferates when the circuit depth is at least a constant critical value.
We introduce a two-dimensional, depth-2, "coarse-grained" circuit architecture, composed of random Clifford gates acting on O(log n) qubits.
arXiv Detail & Related papers (2024-07-30T21:39:23Z) - Universal quantum frequency comb measurements by spectral mode-matching [39.58317527488534]
We present the first general approach to make arbitrary, one-shot measurements of a multimode quantum optical source.
This approach uses spectral mode-matching, which can be understood as interferometry with a memory effect.
arXiv Detail & Related papers (2024-05-28T15:17:21Z) - Characterizing randomness in parameterized quantum circuits through expressibility and average entanglement [39.58317527488534]
Quantum Circuits (PQCs) are still not fully understood outside the scope of their principal application.
We analyse the generation of random states in PQCs under restrictions on the qubits connectivities.
We place a connection between how steep is the increase on the uniformity of the distribution of the generated states and the generation of entanglement.
arXiv Detail & Related papers (2024-05-03T17:32:55Z) - Universal spectral correlations in interacting chaotic few-body quantum
systems [0.0]
We study correlations in terms of the spectral form factor and its moments in interacting chaotic few- and many-body systems.
We find a universal transition from the non-interacting to the strongly interacting case, which can be described as a simple combination of these two limits.
arXiv Detail & Related papers (2023-02-20T12:49:59Z) - Approximate separation of quantum gates and separation experiments of
CNOT based on Particle Swarm Optimization algorithm [1.4821822452801385]
Ying conceived of using two or more small-capacity quantum computers to produce a larger-capacity quantum computing system.
Main obstacle is separating the quantum gates in the whole circuit to produce a tensor product of the local gates.
arXiv Detail & Related papers (2022-01-15T08:10:22Z) - Generalized quantum measurements with matrix product states:
Entanglement phase transition and clusterization [58.720142291102135]
We propose a method for studying the time evolution of many-body quantum lattice systems under continuous and site-resolved measurement.
We observe a peculiar phenomenon of measurement-induced particle clusterization that takes place only for frequent moderately strong measurements, but not for strong infrequent measurements.
arXiv Detail & Related papers (2021-04-21T10:36:57Z) - Quantum particle across Grushin singularity [77.34726150561087]
We study the phenomenon of transmission across the singularity that separates the two half-cylinders.
All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection.
This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
arXiv Detail & Related papers (2020-11-27T12:53:23Z) - Random quantum circuits anti-concentrate in log depth [118.18170052022323]
We study the number of gates needed for the distribution over measurement outcomes for typical circuit instances to be anti-concentrated.
Our definition of anti-concentration is that the expected collision probability is only a constant factor larger than if the distribution were uniform.
In both the case where the gates are nearest-neighbor on a 1D ring and the case where gates are long-range, we show $O(n log(n)) gates are also sufficient.
arXiv Detail & Related papers (2020-11-24T18:44:57Z) - Floquet theory for temporal correlations and spectra in time-periodic
open quantum systems: Application to squeezed parametric oscillation beyond
the rotating-wave approximation [0.0]
We propose a method to compute two-time correlations and corresponding spectral densities of time-periodic open quantum systems.
We show how the quantum Langevin equations for the fluctuations can be efficiently integrated by partitioning the time domain into one-period duration intervals.
arXiv Detail & Related papers (2020-05-17T13:25:04Z) - Boundaries of quantum supremacy via random circuit sampling [69.16452769334367]
Google's recent quantum supremacy experiment heralded a transition point where quantum computing performed a computational task, random circuit sampling.
We examine the constraints of the observed quantum runtime advantage in a larger number of qubits and gates.
arXiv Detail & Related papers (2020-05-05T20:11:53Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.