Digital quantum simulation of open quantum systems using quantum imaginary time evolution

Kamakari, Hirsh; Sun, Shi-Ning; Motta, Mario; Minnich, Austin J.

doi:10.48550/arxiv.2104.07823

Cited by 11 publications

(15 citation statements)

References 54 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Although many quantum algorithms are known for the simulation of closed quantum systems, fewer studies have considered the simulation of open quantum systems despite their rich and interesting behavior [5]. Current approaches include using inherent qubit decoherence [6,7,8], direct simulation of an environment [9,10,11], implementing Kraus maps / Lindblad operators [12,13,14,15,16], variational techniques [17,18], and more [19,20]. Since Barreiro et al first demonstrated their open-system quantum simulator [21], current early-stage dissipative simulations of quantum systems in the areas of quantum chemistry and physics [19,12,7,22] have been completed.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Demonstrating robust simulation of driven-dissipative problems on near-term quantum computers

Rost,

Del Re,

Earnest

et al. 2021

Preprint

View full text Add to dashboard Cite

Quantum computers are poised to revolutionize the simulation of quantum-mechanical systems in physics and chemistry. Current quantum computers execute their algorithms imperfectly, due to uncorrected noise, gate errors, and decoherence. This severely limits the size and scope of protocols which can be run on near-term quantum hardware. Much research has been focused on building more robust hardware to address this issue, however the advantages of more robust algorithms remains largely unexplored. Here we show that algorithms for solving the driven-dissipative many-body problem, among the hardest problems in quantum mechanics, are inherently robust against errors. We find it is possible to solve dissipative problems requiring deep circuits on current quantum devices due to the contractive nature of their time evolution maps. We simulate one thousand steps of time evolution for the non-interacting limit of the infinite driven-dissipative Hubbard model, calculate the current through the system and prepare a thermal state of the atomic limit of the Hubbard model. These problems were solved using circuits containing up to two thousand entangling gates on quantum computers made available by IBM, showing no signs of decreasing fidelity at long times. Our results demonstrate that algorithms for simulating dissipative problems are able to far out-perform similarly complex non-dissipative algorithms on noisy hardware. Our two algorithmic primitives are the basic building blocks of many condensedmatter-physics systems, and we anticipate their demonstrated robustness to hold when generalized to solve the full many-body driven-dissipative quantum problem. Building upon the algorithms presented here may prove to be the most promising approach to tackle important, classically intractable problems on quantum computers before error correction is available.

show abstract

Section: Introductionmentioning

confidence: 99%

“…Here ε s ≡ −2 cos(k + Ωs∆t) is the dispersion relation, n F [x] is the Fermi-Dirac distribution, and the angles at step s are defined byθ s = 2 sin −1 2Γ∆t e βεs + 1and φ s = 2 sin −1 2Γ∆t e −βεs + 1 (S 19). …”

mentioning

confidence: 99%

Demonstrating robust simulation of driven-dissipative problems on near-term quantum computers

Rost,

Del Re,

Earnest

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…An intriguing question to be explored is the role of interaction entering the unitary Hamiltonian for the entanglement transitions in various many-body problems. An experimental implementation of the open quantum Ising chain on IBM's quantum hardware was realized very recently [70]. 1, but for M = 0.5, P = 1 and ∆ = 0, such that the system is non-interacting.…”

Section: Summary and Discussionmentioning

confidence: 99%

Generalized quantum measurements with matrix product states: Entanglement phase transition and clusterization

Doggen,

Gefen,

Gornyi

et al. 2021

Preprint

View full text Add to dashboard Cite

We propose a method, based on matrix product states, for studying the time evolution of manybody quantum lattice systems under continuous and site-resolved measurement. Both the frequency and the strength of generalized measurements can be varied within our scheme, thus allowing us to explore the corresponding two-dimensional phase diagram. The method is applied to one-dimensional chains of nearest-neighbor interacting hard-core bosons. A transition from an entangling to a disentangling (area-law) phase is found. However, by resolving time-dependent density correlations in the monitored system, we find important differences between different regions at the phase boundary. In particular, 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.

show abstract

“…It had the advantage compared to a variational quantum eigensolver (VQE) of not using ancilla qubits. The method was applied to the quantum computation of chemical energy levels on NISQ hardware [32][33][34][35], and the simulation of open quantum systems [36]. The impact of noise on QITE in NISQ hardware was addressed in [37] using error mitigation and randomized compiling.…”

Section: Introductionmentioning

confidence: 99%

Solving MaxCut with Quantum Imaginary Time Evolution

Rizwanul¹,

Siopsis²,

Herrman³

et al. 2022

Preprint

View full text Add to dashboard Cite

We introduce a method to solve the MaxCut problem efficiently based on quantum imaginary time evolution (QITE). We employ a linear Ansatz for unitary updates and an initial state that involve no entanglement. We apply the method to graphs with number of vertices |V | = 4, 6, 8, 10 and show that after ten QITE steps, the average solution is 100%, 99%, 98%, 97%, respectively, of the maximum MaxCut solution. By employing an imaginary-time-dependent Hamiltonian interpolating between a given graph and a subgraph with two edges excised, we show that the modified algorithm has a 100% performance converging to the maximum solution of the MaxCut problem for all graphs up to eight vertices as well as about 100 random samples of ten-vertex graphs. This improved method has an overhead which is polynomial in the number of vertices.

show abstract

Digital quantum simulation of open quantum systems using quantum imaginary time evolution

Cited by 11 publications

References 54 publications

Demonstrating robust simulation of driven-dissipative problems on near-term quantum computers

Demonstrating robust simulation of driven-dissipative problems on near-term quantum computers

Generalized quantum measurements with matrix product states: Entanglement phase transition and clusterization

Solving MaxCut with Quantum Imaginary Time Evolution

Contact Info

Product

Resources

About