Driven-dissipative quantum mechanics on a lattice: Simulating a fermionic reservoir on a quantum computer

Re, Lorenzo Del; Rost, Brian; Kemper, A. F.; Freericks, J. K.

doi:10.1103/physrevb.102.125112

Cited by 51 publications

(30 citation statements)

References 39 publications

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“…1 and described in supplement 5, which is also compared against the ideal circuit and theoretical results from Lindblad techniques, as described in Ref. [28]. As shown in the inset of Fig.…”

Section: Non-interacting Limitmentioning

confidence: 98%

“…From the Kraus map given in Eq. 5 the quantum circuit can be constructed [28] and appears in Fig. 1(d).…”

Section: Non-interacting Limitmentioning

confidence: 99%

“…We build our dissipative circuit by using Kraus operators that induce transitions between computational basis states, which are the energy eigenstates. These transitions are implemented by mapping the system state to an ancilla register and rotating the system qubits controlled on the ancilla [29,28] (shown in Fig. 3(a)); the approach uses just the transitions that correspond to a cycle through the states (depicted in Fig.…”

Section: Atomic Limitmentioning

confidence: 99%

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

Rost,

Del Re,

Earnest

et al. 2021

Preprint

Self Cite

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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.

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Section: Non-interacting Limitmentioning

confidence: 98%

“…From the Kraus map given in Eq. 5 the quantum circuit can be constructed [28] and appears in Fig. 1(d).…”

Section: Non-interacting Limitmentioning

confidence: 99%

Section: Atomic Limitmentioning

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

Self Cite

View full text Add to dashboard Cite

show abstract

“…Several efforts have been made to simulate dissipative-quantum systems. For examples, Barreiro et al experimentally implement open-system dynamics through the dissipative map 32 ; Hu et al propose and demonstrate a general quantum algorithm to evolve open quantum by simulating Kraus maps 33 ; Rost et al simulate condensed matter system 34 ; Viyuela et al prepare topological thermal states to simulate a topological insulator open system for the topological-Uhlmann-phase measurement 35 . In recent years, non-Hermitian quantum mechanics and related systems are investigated massively.…”

Section: Introducitionmentioning

confidence: 99%

Universal quantum simulation of single-qubit nonunitary operators using duality quantum algorithm

Zheng

2021

Sci Rep

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Quantum information processing enhances human’s power to simulate nature in quantum level and solve complex problem efficiently. During the process, a series of operators is performed to evolve the system or undertake a computing task. In recent year, research interest in non-Hermitian quantum systems, dissipative-quantum systems and new quantum algorithms has greatly increased, which nonunitary operators take an important role in. In this work, we utilize the linear combination of unitaries technique for nonunitary dynamics on a single qubit to give explicit decompositions of the necessary unitaries, and simulate arbitrary time-dependent single-qubit nonunitary operator F(t) using duality quantum algorithm. We find that the successful probability is not only decided by F(t) and the initial state, but also is inversely proportional to the dimensions of the used ancillary Hilbert subspace. In a general case, the simulation can be achieved in both eight- and six-dimensional Hilbert spaces. In phase matching conditions, F(t) can be simulated by only two qubits. We illustrate our method by simulating typical non-Hermitian systems and single-qubit measurements. Our method can be extended to high-dimensional case, such as Abrams–Lloyd’s two-qubit gate. By discussing the practicability, we expect applications and experimental implementations in the near future.

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“…A recent emphasis has been using quantum computers to treat classically challenging chemistry and condensed matter problems [5][6][7][8][9]. Advances in near-term quantum hardware now make prototype versions of these simulations possible, for instance in the computation of the ground state properties of chemical [10][11][12][13][14][15][16][17] and solid-state [12,[18][19][20] quantum systems as well as simulation of their real-time dynamics for closed [21][22][23][24][25][26][27][28][29][30][31] and open [32][33][34][35][36][37][38] systems. Several recent studies have also reported the simulation of finite-temperature physics on near-term devices [39][40][41][42].…”

Section: Introductionmentioning

confidence: 99%

Realizing symmetry-protected topological phases in a spin-1/2 chain with next-nearest neighbor hopping on superconducting qubits

Tan¹,

Tazhigulov²,

Chan³

et al. 2021

Preprint

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The realization of novel phases of matter on quantum simulators is a topic of intense interest.Digital quantum computers offer a route to prepare topological phases with interactions that do not naturally arise in analog quantum simulators. Here, we report the realization of symmetryprotected topological (SPT) phases of a spin-1/2 Hamiltonian with next-nearest-neighbor hopping on up to 11 qubits on a programmable superconducting quantum processor. We observe clear signatures of the two distinct SPT phases, such as excitations localized to specific edges and finite string order parameters. Our work advances ongoing efforts to realize novel states of matter with exotic interactions on digital near-term quantum computers.

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Driven-dissipative quantum mechanics on a lattice: Simulating a fermionic reservoir on a quantum computer

Cited by 51 publications

References 39 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

Universal quantum simulation of single-qubit nonunitary operators using duality quantum algorithm

Realizing symmetry-protected topological phases in a spin-1/2 chain with next-nearest neighbor hopping on superconducting qubits

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