Low-depth simulations of fermionic systems on square-grid quantum hardware

Algaba, Manuel G.; Sriluckshmy, P. V.; Leib, Martin; Šimkovic, F.

doi:10.48550/arxiv.2302.01862

Cited by 3 publications

(3 citation statements)

References 76 publications

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“…While we present only a few use cases, the decomposition is universal and can be used to provide low-depth circuits for a wide range of near-term quantum applications. In a recent publication [34] some of the authors use the decomposition technique for fermionic systems and develop additional strategies of gates with optimal fermion-to-qubit mapping to reduce the depth of the circuit further.…”

Section: Discussionmentioning

confidence: 99%

Optimal, hardware native decomposition of parameterized multi-qubit Pauli gates

Sriluckshmy,

Pina-Canelles,

Ponce

et al. 2023

Quantum Sci. Technol.

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We show how to efficiently decompose a parameterized multi-qubit Pauli (PMQP) gate into native parameterized two-qubit Pauli (P2QP) gates minimizing both the circuit depth and the number of P2QP gates. Given a realistic quantum computational model, we argue that the technique is optimal in terms of the number of hardware native gates and the overall depth of the decomposition. Starting from PMQP gate decompositions for the path and star hardware graph, we generalize the procedure to any generic hardware graph and provide exact expressions for the depth and number of P2QP gates of the decomposition. Furthermore, we show how to efficiently combine the decomposition of multiple PMQP gates to further reduce the depth as well as the number of P2QP gates for a combinatorial optimization problem using the Lechner–Hauke–Zoller mapping.

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Section: Discussionmentioning

confidence: 99%

Optimal, hardware native decomposition of parameterized multi-qubit Pauli gates

Sriluckshmy,

Pina-Canelles,

Ponce

et al. 2023

Quantum Sci. Technol.

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“…when doing time evolution), the unitary operator can be realized with a quantum circuit that has single-qubit gates and two-qubit gates following standard decomposition methods [29]. Efficient algorithms for the decomposition of the exponential of multi-σ z operators into quantum circuits are standard in most quantum compilation frameworks and are the subject of intense research to improve the performance of quantum hardware [30,31].…”

Section: Interaction Partmentioning

confidence: 99%

Toward QCD on quantum computer: orbifold lattice approach

Bergner,

Hanada,

Rinaldi

et al. 2024

J. High Energ. Phys.

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We propose an orbifold lattice formulation of QCD suitable for quantum simulations. We show explicitly how to encode gauge degrees of freedom into qubits using noncompact variables, and how to write down a simple truncated Hamiltonian in the coordinate basis. We show that SU(3) gauge group variables and quarks in the fundamental representation can be implemented straightforwardly on qubits, for arbitrary truncation of the gauge manifold.

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“…There are also proposals that utilize defects of surface codes for fermionic quantum simulation [31][32][33], and those defects are recently implemented by Google Quantum AI [34]. Variants of these mappings have been studied to optimize different costs [35][36][37][38][39][40][41][42][43][44][45][46][47][48]. In the context of quantum many-body physics, these mappings also reveal the deep connections between fermion and spin systems [49,50].…”

Section: Introductionmentioning

confidence: 99%

Error-correcting codes for fermionic quantum simulation

Chen,

Gorshkov,

2024

SciPost Phys.

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Utilizing the framework of \mathbb{Z}_2ℤ2 lattice gauge theories in the context of Pauli stabilizer codes, we present methodologies for simulating fermions via qubit systems on a two-dimensional square lattice. We investigate the symplectic automorphisms of the Pauli module over the Laurent polynomial ring. This enables us to systematically increase the code distances of stabilizer codes while fixing the rate between encoded logical fermions and physical qubits. We identify a family of stabilizer codes suitable for fermion simulation, achieving code distances of d=2,3,4,5,6,7, allowing correction of any \lfloor \frac{d-1}{2} \rfloor⌊d−12⌋-qubit error. In contrast to the traditional code concatenation approach, our method can increase the code distances without decreasing the (fermionic) code rate. In particular, we explicitly show all stabilizers and logical operators for codes with code distances of d=3,4,5. We provide syndromes for all Pauli errors and invent a syndrome-matching algorithm to compute code distances numerically.

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Low-depth simulations of fermionic systems on square-grid quantum hardware

Cited by 3 publications

References 76 publications

Optimal, hardware native decomposition of parameterized multi-qubit Pauli gates

Optimal, hardware native decomposition of parameterized multi-qubit Pauli gates

Toward QCD on quantum computer: orbifold lattice approach

Error-correcting codes for fermionic quantum simulation

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