Crossing a topological phase transition with a quantum computer

Smith, Adam; Jobst, B.; Green, Andrew G.; Pollmann, Frank

doi:10.1103/physrevresearch.4.l022020

Cited by 58 publications

(36 citation statements)

References 39 publications

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“…[21] has potentially only constant overhead in circuit depth if the staircase of state and MPO unitaries are aligned (in a similar manner to the interferometric measurement of topological string order parameters in Ref. [15]).…”

Section: Discussionmentioning

confidence: 99%

“…We approach this problem using one-dimensional sequential quantum circuits [23] inspired by matrix product states [15][16][17][31][32][33]. Fig.…”

Section: B Groundstate Optimisationmentioning

confidence: 99%

“…In this work we focus on bond order D = 2 [31][32][33] described by a staircase of two-qubit unitaries, U . Higher bond orders can be achieved with an efficient shallow circuit representation [15,17]. A crucial feature of these circuits is that although the fully translationally invariant state is infinitely deep and infinitely wide, local observables can be measured on a finite-depth, finite-width circuit with an additional unitary V ≡ V (U ) describing the effect of distant parts of the system on the local observables.…”

Section: B Groundstate Optimisationmentioning

confidence: 99%

“…As well as providing the best classical numerical approach for many spin systems, tensor network methods can be directly translated to quantum circuits [13][14][15][16][17]. Doing so has potential quantum advantage over the classical implementations [16], and tensor networks allow initialisation and improvement of quantum circuits in a way that can circumvent the barren plateaux that potentially plague quantum circuits.…”

Section: Introductionmentioning

confidence: 99%

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Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer

Dborin,

Wimalaweera,

Barratt

et al. 2022

Preprint

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We optimise a translationally invariant, sequential quantum circuit on a superconducting quantum device to simulate the groundstate of the quantum Ising model through its quantum critical point. We further demonstrate how the dynamical quantum critical point found in quenches of this model across its quantum critical point can be simulated. Our approach avoids finite-size scaling effects by using sequential quantum circuits inspired by infinite matrix product states. We provide efficient circuits and a variety of error mitigation strategies to implement, optimise and time-evolve these states. CONTENTS I. Introduction 1 II. Results 2 A. Quantum Phase Transitions 3 B. Groundstate Optimisation 3 C. Calculating and Optimising Overlaps 5 D. Quantum Dynamics 6 III. Discussion 7 IV. Methods 8 A. Fixed-point equations 8 B. Error Mitigation Strategies 8 References 9

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Section: Discussionmentioning

confidence: 99%

“…We approach this problem using one-dimensional sequential quantum circuits [23] inspired by matrix product states [15][16][17][31][32][33]. Fig.…”

Section: B Groundstate Optimisationmentioning

confidence: 99%

Section: B Groundstate Optimisationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer

Dborin,

Wimalaweera,

Barratt

et al. 2022

Preprint

Self Cite

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show abstract

“…Previous work in this context has focused on recognizing topological quantum phases from (simulated) measurement data using classical machine learning techniques 35 – 38 . Furthermore, topological states have recently been prepared on quantum hardware and analyzed by measuring characteristic observables 39 – 41 such as string order parameters. Here, we experimentally demonstrate a new paradigm to detect symmetry-protected topological states on a 7-qubit quantum device by preparing quantum states within and outside of the SPT phase and by further processing these states with a quantum convolutional neural network to perform quantum phase recognition.…”

Section: Introductionmentioning

confidence: 99%

Realizing quantum convolutional neural networks on a superconducting quantum processor to recognize quantum phases

et al. 2022

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Quantum computing crucially relies on the ability to efficiently characterize the quantum states output by quantum hardware. Conventional methods which probe these states through direct measurements and classically computed correlations become computationally expensive when increasing the system size. Quantum neural networks tailored to recognize specific features of quantum states by combining unitary operations, measurements and feedforward promise to require fewer measurements and to tolerate errors. Here, we realize a quantum convolutional neural network (QCNN) on a 7-qubit superconducting quantum processor to identify symmetry-protected topological (SPT) phases of a spin model characterized by a non-zero string order parameter. We benchmark the performance of the QCNN based on approximate ground states of a family of cluster-Ising Hamiltonians which we prepare using a hardware-efficient, low-depth state preparation circuit. We find that, despite being composed of finite-fidelity gates itself, the QCNN recognizes the topological phase with higher fidelity than direct measurements of the string order parameter for the prepared states.

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Finding eigenvectors with a quantum variational algorithm

Garcia-Escartin

2024

Quantum Inf Process

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This paper presents a hybrid variational quantum algorithm that finds a random eigenvector of a unitary matrix with a known quantum circuit. The algorithm is based on the SWAP test on trial states generated by a parametrized quantum circuit. The eigenvector is described by a compact set of classical parameters that can be used to reproduce the found approximation to the eigenstate on demand. This variational eigenvector finder can be adapted to solve the generalized eigenvalue problem, to find the eigenvectors of normal matrices and to perform quantum principal component analysis on unknown input mixed states. These algorithms can all be run with low-depth quantum circuits, suitable for an efficient implementation on noisy intermediate-scale quantum computers and, with some restrictions, on linear optical systems. In full-scale quantum computers, where there might be optimization problems due to barren plateaus in larger systems, the proposed algorithms can be used as a primitive to boost known quantum algorithms. Limitations and potential applications are discussed.

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Crossing a topological phase transition with a quantum computer

Cited by 58 publications

References 39 publications

Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer

Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer

Realizing quantum convolutional neural networks on a superconducting quantum processor to recognize quantum phases

Finding eigenvectors with a quantum variational algorithm

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