Many-body thermodynamics on quantum computers via partition function zeros

Francis, Akhil; Zhu, Daiwei; Alderete, C. Huerta; Johri, Sonika; Xiao, Xiao; Freericks, J. K.; Monroe, Christopher; Linke, Norbert; Kemper, A. F.

doi:10.1126/sciadv.abf2447

Cited by 40 publications

(27 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[49] It is noted here that there exist quantum algorithms for obtaining the complex partition functions for analyses of quantum critical phenomena. [50][51][52]…”

Section: ✌ ✌mentioning

confidence: 99%

Probabilistic imaginary-time evolution by using forward and backward real-time evolution with a single ancilla: first-quantized eigensolver of quantum chemistry for ground states

Kosugi¹,

Nishiya²,

Matsushita³

2021

Preprint

View full text Add to dashboard Cite

Imaginary-time evolution (ITE) on a quantum computer is a promising formalism for obtaining the ground state of a quantum system. As a kind of it, the probabilistic ITE (PITE) takes advantage of measurements to implement the nonunitary operations. We propose a new approach of PITE which requires only a single ancillary qubit. Under a practical approximation, the circuit is constructed from the forward and backward real-time evolution (RTE) gates as black boxes, generated by the original many-qubit Hamiltonian. All the efficient unitary quantum algorithms for RTE proposed so far and those in the future can thus be transferred to ITE exactly as they are. Our approach can also be used for obtaining the Gibbs state at a finite temperature and the partition function. We apply the approach to several systems as illustrative examples to see its validity. We also discuss the application of our approach to quantum chemistry by focusing on the scaling of computational cost, leading to a novel framework denoted by first-quantized quantum eigensolver.

show abstract

“…[49] It is noted here that there exist quantum algorithms for obtaining the complex partition functions for analyses of quantum critical phenomena. [50][51][52]…”

Section: ✌ ✌mentioning

confidence: 99%

Probabilistic imaginary-time evolution by using forward and backward real-time evolution with a single ancilla: first-quantized eigensolver of quantum chemistry for ground states

Kosugi¹,

Nishiya²,

Matsushita³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…9,11,[13][14][15] In recent years, digital and analog quantum simulators have emerged as a promising platform for the simulation of quantum phenomena. Quantum simulators have already been used to study phase transitions using the method of partition function zeros 16 and the Kibble-Zurek mechanism. 17,18 In this paper, we present a protocol to implement the finite-size scaling method on a digital quantum simulator.…”

Section: Introductionmentioning

confidence: 99%

Finite-Size Scaling on a Digital Quantum Simulator using Quantum Restricted Boltzmann Machine

Khalid¹,

Sureshbabu²,

Banerjee³

et al. 2022

Preprint

View full text Add to dashboard Cite

The critical point and the critical exponents for a phase transition can be determined using the Finite-Size Scaling (FSS) analysis. This method assumes that the phase transition occurs only in the infinite size limit. However, there has been a lot of interest recently in quantum phase transitions occuring in finite size systems such as a single two-level system interacting with a single bosonic mode e.g. in the Quantum Rabi Model (QRM). Since, these phase transitions occur at a finite system size, the traditional FSS method is rendered inapplicable for these cases. For cases like this, we propose an alternative FSS method in which the truncation of the system is done in the Hilbert space instead of the physical space. This approach has previously been used to calculate the critical parameters for stability and symmetry breaking of electronic 1

show abstract

“…However, environments tend to be very large, and directly simulating a system coupled to an environment using classical or quantum simulation requires approximations and many extra degrees of freedom to serve as a source of entropy. Sampling from difficult distributions like a multivariate Gibbs distribution on quantum computers has been proposed using Metropolis sampling algorithms that reduce time complexity [1][2][3][4][5], variational algorithms that are possibly well-suited to near-term quantum computers but have a classical optimization overhead [6,7], thermal-field double states [8,9], and quantum imaginary time-evolution to implement the minimally entangled typical thermal state (METTS) [10,11] sampling algorithm on quantum computers [12,13]. Our approach is different, as we engineer an open-quantum system with the desired thermal/Gibbs state as the fixed point of evolution.…”

Section: Introductionmentioning

confidence: 99%

Quantum Markov Chain Monte Carlo with Digital Dissipative Dynamics on Quantum Computers

Metcalf¹,

Stone²,

Klymko³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

Modeling the dynamics of a quantum system connected to the environment is critical for advancing our understanding of complex quantum processes, as most quantum processes in nature are affected by an environment. Modeling a macroscopic environment on a quantum simulator may be achieved by coupling independent ancilla qubits that facilitate energy exchange in an appropriate manner with the system and mimic an environment. This approach requires a large, and possibly exponential number of ancillary degrees of freedom which is impractical. In contrast, we develop a digital quantum algorithm that simulates interaction with an environment using a small number of ancilla qubits. By combining periodic modulation of the ancilla energies, or spectral combing, with periodic reset operations, we are able to mimic interaction with a large environment and generate thermal states of interacting many-body systems. We evaluate the algorithm by simulating preparation of thermal states of the transverse Ising model. Our algorithm can also be viewed as a quantum Markov chain Monte Carlo (QMCMC) process that allows sampling of the Gibbs distribution of a multivariate model. To demonstrate this we evaluate the accuracy of sampling Gibbs distributions of simple probabilistic graphical models using the algorithm.

show abstract

Many-body thermodynamics on quantum computers via partition function zeros

Cited by 40 publications

References 52 publications

Probabilistic imaginary-time evolution by using forward and backward real-time evolution with a single ancilla: first-quantized eigensolver of quantum chemistry for ground states

Probabilistic imaginary-time evolution by using forward and backward real-time evolution with a single ancilla: first-quantized eigensolver of quantum chemistry for ground states

Finite-Size Scaling on a Digital Quantum Simulator using Quantum Restricted Boltzmann Machine

Quantum Markov Chain Monte Carlo with Digital Dissipative Dynamics on Quantum Computers

Contact Info

Product

Resources

About