Hardware-efficient variational quantum algorithms for time evolution

Benedetti, Marcello; Fiorentini, Mattia; Lubasch, Michael

doi:10.1103/physrevresearch.3.033083

Cited by 136 publications

(71 citation statements)

References 50 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Hence, trapped-ion quantum processors may benefit from the combination of F-VQE with causal cones [13]. Causal cones can split the evaluation of the cost function into batches of circuits with fewer qubits [41]. This allows quantum computers to tackle combinatorial optimization problems with more variables than their physical qubits and parallelize the workload.…”

Section: Discussionmentioning

confidence: 99%

A case study of variational quantum algorithms for a job shop scheduling problem

Amaro

Rosenkranz

Fitzpatrick

et al. 2022

EPJ Quantum Technol.

Self Cite

View full text Add to dashboard Cite

Combinatorial optimization models a vast range of industrial processes aiming at improving their efficiency. In general, solving this type of problem exactly is computationally intractable. Therefore, practitioners rely on heuristic solution approaches. Variational quantum algorithms are optimization heuristics that can be demonstrated with available quantum hardware. In this case study, we apply four variational quantum heuristics running on IBM’s superconducting quantum processors to the job shop scheduling problem. Our problem optimizes a steel manufacturing process. A comparison on 5 qubits shows that the recent filtering variational quantum eigensolver (F-VQE) converges faster and samples the global optimum more frequently than the quantum approximate optimization algorithm (QAOA), the standard variational quantum eigensolver (VQE), and variational quantum imaginary time evolution (VarQITE). Furthermore, F-VQE readily solves problem sizes of up to 23 qubits on hardware without error mitigation post processing.

show abstract

Section: Discussionmentioning

confidence: 99%

A case study of variational quantum algorithms for a job shop scheduling problem

Amaro

Rosenkranz

Fitzpatrick

et al. 2022

EPJ Quantum Technol.

Self Cite

View full text Add to dashboard Cite

show abstract

“…However, quantum ITE using McLachlan's principle is typically expensive to implement because of the required metric tensor computations and matrix inversion [240,348]. Benedetti et al developed an alternative method for VarQITE that avoids these computations and is gradient free [40]. Their variational time evolution approach is also applicable to real-time evolution.…”

Section: Variational Quantum Imaginary Time Evolution (Varqite)mentioning

confidence: 99%

A Survey of Quantum Computing for Finance

Herman¹,

Googin²,

Liu³

et al. 2022

Preprint

View full text Add to dashboard Cite

Quantum computers are expected to surpass the computational capabilities of classical computers during this decade and have transformative impact on numerous industry sectors, particularly finance. In fact, finance is estimated to be the first industry sector to benefit from quantum computing, not only in the medium and long terms, but even in the short term. This survey paper presents a comprehensive summary of the state of the art of quantum computing for financial applications, with particular emphasis on Monte Carlo integration, optimization, and machine learning, showing how these solutions, adapted to work on a quantum computer, can help solve more efficiently and accurately problems such as derivative pricing, risk analysis, portfolio optimization, natural language processing, and fraud detection. We also discuss the feasibility of these algorithms on near-term quantum computers with various hardware implementations and demonstrate how they relate to a wide range of use cases in finance. We hope this article will not only serve as a reference for academic researchers and industry practitioners but also inspire new ideas for future research.

show abstract

“…Noting that (U A ⊗ V * B ) |Φ + AB = (U A V † A ⊗ I B ) |Φ + AB and Π j can be decomposed as a sum of Pauli operator by Eq. (29), it is sufficient to evaluate…”

Section: Appendixmentioning

confidence: 99%

“…Another promising approach is to use the framework of variational quantum algorithms [24]. They are exemplified by variational quantum simulation [25][26][27][28][29][30][31], and quantum compilations FIG. 1.…”

Section: Introductionmentioning

confidence: 99%

Local variational quantum compilation of a large-scale Hamiltonian dynamics

Mizuta¹,

Nakagawa²,

Mitarai³

et al. 2022

Preprint

View full text Add to dashboard Cite

Implementing time evolution operators on quantum circuits is important for quantum simulation. However, the standard way, Trotterization, requires a huge numbers of gates to achieve desirable accuracy. Here, we propose a local variational quantum compilation (LVQC) algorithm, which allows to accurately and efficiently compile a time evolution operators on a large-scale quantum system by the optimization with smaller-size quantum systems. LVQC utilizes a subsystem cost function, which approximates the fidelity of the whole circuit, defined for each subsystem as large as approximate causal cones brought by the Lieb-Robinson (LR) bound. We rigorously derive its scaling property with respect to the subsystem size, and show that the optimization conducted on the subsystem size leads to the compilation of whole-system time evolution operators. As a result, LVQC runs with limited-size quantum computers or classical simulators that can handle such smaller quantum systems. For instance, finite-ranged and short-ranged interacting L-size systems can be compiled with O(L 0 )-or O(log L)-size quantum systems depending on observables of interest. Furthermore, since this formalism relies only on the LR bound, it can efficiently construct time evolution operators of various systems in generic dimension involving finite-, short-, and long-ranged interactions. We also numerically demonstrate the LVQC algorithm for one-dimensional systems. Employing classical simulation by time-evolving block decimation, we succeed in compressing the depth of a time evolution operators up to 40 qubits by the compilation for 20 qubits. LVQC not only provides classical protocols for designing large-scale quantum circuits, but also will shed light on applications of intermediate-scale quantum devices in implementing algorithms in larger-scale quantum devices.

show abstract

Hardware-efficient variational quantum algorithms for time evolution

Cited by 136 publications

References 50 publications

A case study of variational quantum algorithms for a job shop scheduling problem

A case study of variational quantum algorithms for a job shop scheduling problem

A Survey of Quantum Computing for Finance

Local variational quantum compilation of a large-scale Hamiltonian dynamics

Contact Info

Product

Resources

About