Circuit optimization of Hamiltonian simulation by simultaneous diagonalization of Pauli clusters

Berg, E. van den; Temme, Kristan

doi:10.22331/q-2020-09-12-322

Cited by 30 publications

(14 citation statements)

References 24 publications

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“…Recently, a technique based on partitioning the Pauli strings into commuting sets and then performing simultaneous diagonalisation of each set was proposed in ref. 87 for reducing the gate count in context of Hamiltonian simulation. A similar approach to that of ref.…”

Section: The Unitary Coupled Cluster Ansatz For Quantum Computingmentioning

confidence: 99%

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A quantum computing view on unitary coupled cluster theory

et al. 2022

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Section: The Unitary Coupled Cluster Ansatz For Quantum Computingmentioning

confidence: 99%

“…A similar approach to that of ref. 87 is proposed in ESI,† which reduces the CNOT gate count by more than 50% and removes the compiling bottlenecks of partition into commuting Pauli strings or complex compilation algorithms.…”

Section: The Unitary Coupled Cluster Ansatz For Quantum Computingmentioning

confidence: 99%

A quantum computing view on unitary coupled cluster theory

et al. 2022

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“…Recently, a technique based on partitioning the Pauli strings into commuting sets and then performing simultaneous diagonalisation of each set was proposed in Ref. [70] for reducing the gate count in context of Hamiltonian simulation. A similar approach to that of Ref.…”

Section: E Compilation Strategiesmentioning

confidence: 99%

A Quantum Computing View on Unitary Coupled Cluster Theory

Anand,

Schleich,

Alperin-Lea

et al. 2021

Preprint

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We present a review of the Unitary Coupled Cluster (UCC) ansatz and related ansätze which are used to variationally solve the electronic structure problem on quantum computers. A brief history of coupled cluster (CC) methods is provided, followed by a broad discussion of the formulation of CC theory. This includes touching on the merits and difficulties of the method and several variants, UCC among them, in the classical context, to motivate their applications on quantum computers. In the core of the text, the UCC ansatz and its implementation on a quantum computer are discussed at length, in addition to a discussion on several derived and related ansätze specific to quantum computing. The review concludes with a unified perspective on the discussed ansätze, attempting to bring them under a common framework, as well as with a reflection upon open problems within the field. CONTENTS I. IntroductionA. A brief history of Coupled Cluster theory B. Assumed background and notation conventions C. Coupled Cluster theory 1. Formulation 2. Projective approaches 3. Variational approaches 4. Moving beyond the classical II. Estimating energies on quantum computers A. Quantum Phase Estimation B. Variational Quantum Eigensolver C. Tackling challenges within QPE and VQE by UCC III. The Unitary Coupled Cluster ansatz for quantum computing A. Fermionic excitations: The basic building blocks B. Qubit perspective on fermionic excitations C. Commutativity of subterms in fermionic excitation operators

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“…Extracting a circuit back out of an arbitrary PDDAG can be naively done by synthesising the stabilizer tableau [1,26] and each of the Pauli exponentials in turn according to some topological ordering using some standard decompositions [6,11] although this will typically add an extremely high amount of redundant Clifford gates. More efficient synthesis can be performed using techniques for synthesising pairs of rotations simultaneously [11] or by diagonalising sets of mutually commuting rotations [8,12]. It is also possible that future architectures may find efficient ways to perform each Pauli rotation natively or employ lattice surgery where it is practical to just perform them directly [24].…”

Section: Definition 33 (Pauli Dependency Dag)mentioning

confidence: 99%

Relating Measurement Patterns to Circuits via Pauli Flow

Simmons¹

2021

Electron. Proc. Theor. Comput. Sci.

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The one-way model of Measurement-Based Quantum Computing and the gate-based circuit model give two different presentations of how quantum computation can be performed. There are known methods for converting any gate-based quantum circuit into a one-way computation, whereas the reverse is only efficient given some constraints on the structure of the measurement pattern. Causal flow and generalised flow have already been shown as sufficient, with efficient algorithms for identifying these properties and performing the circuit extraction. Pauli flow is a weaker set of conditions that extends generalised flow to use the knowledge that some vertices are measured in a Pauli basis. In this paper, we show that Pauli flow can similarly be identified efficiently and that any measurement pattern whose underlying graph admits a Pauli flow can be efficiently transformed into a gate-based circuit without using ancilla qubits. We then use this relationship to derive simulation results for the effects of graph-theoretic rewrites in the ZX-calculus using a more circuit-like data structure we call the Pauli Dependency DAG. Relating Measurement Patterns to Circuits via Pauli Flow Gate Equivalent Pauli exponentials CX ct e −i π 4 Z c X t e i π 4 Z c e i π 4 X t CZ ct e −i π 4 Z c Z t e i π 4 Z c e i π 4 Z t RZ(α) e −i α 2 Z RX (α) e −i α 2 X H e −i π 4 Z e −i π 4 X e −i π 4 Z CCX abt e −i π 8 Z a Z b X t e i π 8 Z a Z b e i π 8 Z a X t e i π 8 Z b X t e −i π 8 Z a e −i π 8 Z b e −i π 8 X t

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Circuit optimization of Hamiltonian simulation by simultaneous diagonalization of Pauli clusters

Cited by 30 publications

References 24 publications

A quantum computing view on unitary coupled cluster theory

A quantum computing view on unitary coupled cluster theory

A Quantum Computing View on Unitary Coupled Cluster Theory

Relating Measurement Patterns to Circuits via Pauli Flow

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