Improved Success Probability with Greater Circuit Depth for the Quantum Approximate Optimization Algorithm

Bengtsson, Andreas; Vikstål, Pontus; Warren, Christopher; Svensson, Marika; Gu, Xiu; Kockum, Anton Frisk; Krantz, Philip; Križan, Christian; Shiri, Daryoush; Svensson, Ida-Maria; Tancredi, Giovanna; Johansson, Göran; Delsing, Per; Ferrini, Giulia; Bylander, Jonas

doi:10.1103/physrevapplied.14.034010

Cited by 88 publications

(81 citation statements)

References 22 publications

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“…This in turn allows us to fully exploit Cross-Entropy Benchmarking and Heavy Output Generation Benchmarking. Here we will argue numerically which of the circuits we introduce in Section 3 generate output probabilities of this form, 23 and discuss the implications when they do not.…”

Section: Data Availabilitymentioning

confidence: 99%

“…The second is for the circuit class to be a particular instance of an application. Such benchmarks have been defined in the context of quantum simulation [12][13][14][15][16], quantum machine learning [10,[17][18][19][20], discrete optimisation [21][22][23][24], and quantum computational supremacy [3,[25][26][27]. This approach has the advantage that the definition of success when running a circuit from the class is fairly straightforward, but with the disadvantage that performance, as measured by one instance of an application, may not be predictive of performance for the application generically, or another application.…”

Section: Introductionmentioning

confidence: 99%

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Application-Motivated, Holistic Benchmarking of a Full Quantum Computing Stack

Mills

Sivarajah

Scholten³

et al. 2021

Quantum

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Quantum computing systems need to be benchmarked in terms of practical tasks they would be expected to do. Here, we propose 3 "application-motivated" circuit classes for benchmarking: deep (relevant for state preparation in the variational quantum eigensolver algorithm), shallow (inspired by IQP-type circuits that might be useful for near-term quantum machine learning), and square (inspired by the quantum volume benchmark). We quantify the performance of a quantum computing system in running circuits from these classes using several figures of merit, all of which require exponential classical computing resources and a polynomial number of classical samples (bitstrings) from the system. We study how performance varies with the compilation strategy used and the device on which the circuit is run. Using systems made available by IBM Quantum, we examine their performance, showing that noise-aware compilation strategies may be beneficial, and that device connectivity and noise levels play a crucial role in the performance of the system according to our benchmarks.

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Section: Data Availabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Application-Motivated, Holistic Benchmarking of a Full Quantum Computing Stack

Mills

Sivarajah

Scholten³

et al. 2021

Quantum

View full text Add to dashboard Cite

show abstract

“…For example, in chemistry calculations the number of particle excitations needs to be preserved, which makes the iSWAP gate the optimal choice [5,6]. For quantum approximate optimization algorithms, on the other hand, a controlled-phase gate is better matched to the computational task [7,8]. Ideally, the quantum computing hardware supports a gate set with multiple types of single-qubit and two-qubit operations.…”

Section: Introductionmentioning

confidence: 99%

“…To benefit from an extended gate set, all gates must be executed with high fidelity. While the tunable coupler supports both fast iSWAP and CZ gates on the same platform with almost identical hardware requirements, gate fidelities around 99% have been reached with the CZ gate [8], but typical iSWAP fidelities remain lower [6,29,36]. Here, we explore both types of gates on the same device, characterize their respective fidelities, and analyze the specific sensitivity of the gates to the various sources of coherent and incoherent errors.…”

Section: Introductionmentioning

confidence: 99%

Benchmarking the noise sensitivity of different parametric two-qubit gates in a single superconducting quantum computing platform

Ganzhorn

Salis

Egger

et al. 2020

Phys. Rev. Research

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The possibility to utilize different types of two-qubit gates on a single quantum computing platform adds flexibility in the decomposition of quantum algorithms. A larger hardware-native gate set may decrease the number of required gates, provided that all gates are realized with high fidelity. Here, we benchmark both controlled-Z (CZ) and exchange-type (iSWAP) gates using a parametrically driven tunable coupler that mediates the interaction between two superconducting qubits. Using randomized benchmarking protocols we estimate an error per gate of 0.9 ± 0.03 and 1.3 ± 0.4% for the CZ and the iSWAP gate, respectively. We argue that spurious ZZ-type couplings are the dominant error source for the iSWAP gate, and that phase stability of all microwave drives is of utmost importance. Such differences in the achievable fidelities for different two-qubit gates have to be taken into account when mapping quantum algorithms to real hardware.

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“…In addition to increasing algorithmic difficulties, the engineering overhead of scaling up the quantum hardware also currently limits the size of computational tasks to toy models. Previously proposed schemes to implement quantum algorithms to solve optimization problems have used a number of classical variables equal to the number of qubits available and were therefore limited to problem sizes involving only a few tens of them [1,5,6,21,36,37,41,42,49]. This is not representative of real-world optimization problems, where the number of classical variables n c involved can be on the order of 10 4 .…”

Section: Introductionmentioning

confidence: 99%

Qubit-efficient encoding schemes for binary optimisation problems

Tan

Lemonde

Thanasilp

et al. 2021

Quantum

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We propose and analyze a set of variational quantum algorithms for solving quadratic unconstrained binary optimization problems where a problem consisting of nc classical variables can be implemented on O(log⁡nc) number of qubits. The underlying encoding scheme allows for a systematic increase in correlations among the classical variables captured by a variational quantum state by progressively increasing the number of qubits involved. We first examine the simplest limit where all correlations are neglected, i.e. when the quantum state can only describe statistically independent classical variables. We apply this minimal encoding to find approximate solutions of a general problem instance comprised of 64 classical variables using 7 qubits. Next, we show how two-body correlations between the classical variables can be incorporated in the variational quantum state and how it can improve the quality of the approximate solutions. We give an example by solving a 42-variable Max-Cut problem using only 8 qubits where we exploit the specific topology of the problem. We analyze whether these cases can be optimized efficiently given the limited resources available in state-of-the-art quantum platforms. Lastly, we present the general framework for extending the expressibility of the probability distribution to any multi-body correlations.

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Improved Success Probability with Greater Circuit Depth for the Quantum Approximate Optimization Algorithm

Cited by 88 publications

References 22 publications

Application-Motivated, Holistic Benchmarking of a Full Quantum Computing Stack

Application-Motivated, Holistic Benchmarking of a Full Quantum Computing Stack

Benchmarking the noise sensitivity of different parametric two-qubit gates in a single superconducting quantum computing platform

Qubit-efficient encoding schemes for binary optimisation problems

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