Related papers: Evaluating thermal expectation values by almost ideal sampling with Trotter gates

Evaluating thermal expectation values by almost ideal sampling with Trotter gates

URL: http://arxiv.org/abs/2209.03523v2
Date: Mon, 16 Jan 2023 01:37:20 GMT
Title: Evaluating thermal expectation values by almost ideal sampling with Trotter gates
Authors: Shimpei Goto, Ryui Kaneko, and Ippei Danshita
Abstract summary: We investigate the sampling efficiency for the simulations of quantum many-body systems at finite temperatures. We find that the sampling efficiency is almost equal to that obtained by a typical pure quantum (TPQ) state method.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We investigate the sampling efficiency for the simulations of quantum many-body systems at finite temperatures when initial sampling states are generated by applying Trotter gates to random phase product states (RPPSs). We restrict the number of applications of Trotter gates to be proportional to the system size, and thus the preparation would be easily accomplished in fault-tolerant quantum computers. When the Trotter gates are made from a nonintegrable Hamiltonian, we observe that the sampling efficiency increases with system size. This trend means that almost ideal sampling of initial states can be achieved in sufficiently large systems. We also find that the sampling efficiency is almost equal to that obtained by a typical pure quantum (TPQ) state method utilizing Haar random sampling in some cases. These findings suggest that chaotic Hamiltonian dynamics can transform RPPSs into an alternative to TPQ states for evaluating thermal expectation values.

Related papers

Optimizing random local Hamiltonians by dissipation [44.99833362998488]
We prove that a simplified quantum Gibbs sampling algorithm achieves a $Omega(frac1k)$-fraction approximation of the optimum. Our results suggest that finding low-energy states for sparsified (quasi)local spin and fermionic models is quantumly easy but classically nontrivial.
arXiv Detail & Related papers (2024-11-04T20:21:16Z)
Quantum computational advantage with constant-temperature Gibbs sampling [1.1930434318557157]
A quantum system coupled to a bath at some fixed, finite temperature converges to its Gibbs state. This thermalization process defines a natural, physically-motivated model of quantum computation. We consider sampling from the measurement outcome distribution of quantum Gibbs states at constant temperatures.
arXiv Detail & Related papers (2024-04-23T00:29:21Z)
Dissipative Quantum Gibbs Sampling [1.5845445933441118]
We show that a dissipative quantum algorithm with a simple, local update rule is able to sample from the quantum Gibbs state. This gives a new answer to the long-sought-after quantum analogue of Metropolis sampling.
arXiv Detail & Related papers (2023-04-10T11:51:50Z)
Sparse random Hamiltonians are quantumly easy [105.6788971265845]
A candidate application for quantum computers is to simulate the low-temperature properties of quantum systems. This paper shows that, for most random Hamiltonians, the maximally mixed state is a sufficiently good trial state. Phase estimation efficiently prepares states with energy arbitrarily close to the ground energy.
arXiv Detail & Related papers (2023-02-07T10:57:36Z)
Importance sampling for stochastic quantum simulations [68.8204255655161]
We introduce the qDrift protocol, which builds random product formulas by sampling from the Hamiltonian according to the coefficients. We show that the simulation cost can be reduced while achieving the same accuracy, by considering the individual simulation cost during the sampling stage. Results are confirmed by numerical simulations performed on a lattice nuclear effective field theory.
arXiv Detail & Related papers (2022-12-12T15:06:32Z)
Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics [62.997667081978825]
We show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality. We show that a finite temperature phase transition in the long-range transverse field Ising model can be characterized in trapped ion quantum simulators.
arXiv Detail & Related papers (2022-06-03T18:00:02Z)
Robust preparation of Wigner-negative states with optimized SNAP-displacement sequences [41.42601188771239]
We create non-classical states of light in three-dimensional microwave cavities. These states are useful for quantum computation. We show that this way of creating non-classical states is robust to fluctuations of the system parameters.
arXiv Detail & Related papers (2021-11-15T18:20:38Z)
Perils of Embedding for Quantum Sampling [0.0]
A common approach is to minor embed the desired Hamiltonian in a native Hamiltonian. Here, we consider quantum thermal sampling in the transverse-field Ising model. We simulate systems of much larger sizes and larger transverse-field strengths than would otherwise be possible.
arXiv Detail & Related papers (2021-03-12T01:49:52Z)
Matrix product state approach for a quantum system at finite temperatures using random phases and Trotter gates [0.0]
We develop a numerical method for simulating quantum many-body systems at finite temperatures without importance sampling. Our method is an extension of the random phase product state (RPPS) approach introduced recently.
arXiv Detail & Related papers (2021-03-08T02:28:24Z)
Assessment of weak-coupling approximations on a driven two-level system under dissipation [58.720142291102135]
We study a driven qubit through the numerically exact and non-perturbative method known as the Liouville-von equation with dissipation. We propose a metric that may be used in experiments to map the regime of validity of the Lindblad equation in predicting the steady state of the driven qubit.
arXiv Detail & Related papers (2020-11-11T22:45:57Z)

This list is automatically generated from the titles and abstracts of the papers in this site.