Benchmarking the quantum approximate optimization algorithm

Willsch, Madita; Willsch, Dennis; Jin, Fengping; Raedt, Hans De; Michielsen, Kristel

doi:10.1007/s11128-020-02692-8

Cited by 137 publications

(109 citation statements)

References 30 publications

(33 reference statements)

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“…Another such example of a two-qubit noise channel, which is explicitly not accounted for in our noise models, is crosstalk. The results in Figure 8 are consistent with the expectation that cross-talk should have 22 These are modelled to consist of a depolarising errors followed by a thermal relaxation errors.…”

Section: Noise Models Under Represent Some Noise Channelssupporting

confidence: 86%

“…For the devices explored here, the noise models are built using Qiskit. They are derived from a device's properties, and include one-and two-qubit gate errors 22 and single-qubit readout errors. We find these noise models are inadequate to explain some of the discrepancies observed in the data.…”

Section: Insights From Classical Simulationmentioning

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: Noise Models Under Represent Some Noise Channelssupporting

confidence: 86%

Section: Insights From Classical Simulationmentioning

confidence: 99%

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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“…Contemporary demonstrations of QAOA serve as benchmarks to enable practically relevant demonstrations of optimization and other quantum algorithms [10,[23][24][25][26][27]. Our results illuminate the first QAOA performance indicators.…”

Section: Introductionmentioning

confidence: 70%

Reachability Deficits in Quantum Approximate Optimization

et al. 2020

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The quantum approximate optimization algorithm (QAOA) has rapidly become a cornerstone of contemporary quantum algorithm development. Despite a growing range of applications, only a few results have been developed towards understanding the algorithms ultimate limitations. Here we report that QAOA exhibits a strong dependence on a problem instances constraint to variable ratio-this problem density places a limiting restriction on the algorithms capacity to minimize a corresponding objective function (and hence solve optimization problems). Such reachability deficits persist even in the absence of barren plateaus [1] and are outside of the recently reported level-1 QAOA limitations [2]. Building on general numerical experiments, we compare the presence of reachability deficits with analytic solutions of the variational model of Grover's search algorithm. Comparing QAOA's performance between random 3-SAT (NP-hard) and 2-SAT (efficiently solved) instances, reachability deficits increased with problem density. *

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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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Benchmarking the quantum approximate optimization algorithm

Cited by 137 publications

References 30 publications

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

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

Reachability Deficits in Quantum Approximate Optimization

Qubit-efficient encoding schemes for binary optimisation problems

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