- Award ID(s):
- 2037984
- NSF-PAR ID:
- 10276496
- Date Published:
- Journal Name:
- npj Quantum Information
- Volume:
- 7
- Issue:
- 1
- ISSN:
- 2056-6387
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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We describe how classical supercomputing can aid unreliable quantum processors of intermediate size to solve large problem instances reliably. We advocate using a hybrid quantum-classical architecture where larger quantum circuits are broken into smaller sub-circuits that are evaluated separately, either using a quantum processor or a quantum simulator running on a classical supercomputer. Circuit compilation techniques that determine which qubits are simulated classically will greatly impact the system performance as well as provide a tradeoff between circuit reliability and runtime. We describe how classical supercomputing can aid unreliable quantum processors of intermediate size to solve large problem instances reliably. We advocate using a hybrid quantum-classical architecture where larger quantum circuits are broken into smaller sub-circuits that are evaluated separately, either using a quantum processor or a quantum simulator running on a classical supercomputer. Circuit compilation techniques that determine which qubits are simulated classically will greatly impact the system performance as well as provide a tradeoff between circuit reliability and runtime.more » « less
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and the corresponding noiseless output distribution$$p_{\text {noisy}}$$ shrink exponentially with the expected number of gate-level errors. Specifically, the linear cross-entropy benchmark$$p_{\text {ideal}}$$ F that measures this correlation behaves as , where$$F=\text {exp}(-2s\epsilon \pm O(s\epsilon ^2))$$ is the probability of error per circuit location and$$\epsilon $$ s is the number of two-qubit gates. Furthermore, if the noise is incoherent—for example, depolarizing or dephasing noise—the total variation distance between the noisy output distribution and the uniform distribution$$p_{\text {noisy}}$$ decays at precisely the same rate. Consequently, the noisy output distribution can be approximated as$$p_{\text {unif}}$$ . In other words, although at least one local error occurs with probability$$p_{\text {noisy}}\approx Fp_{\text {ideal}}+ (1-F)p_{\text {unif}}$$ , the errors are scrambled by the random quantum circuit and can be treated as global white noise, contributing completely uniform output. Importantly, we upper bound the average total variation error in this approximation by$$1-F$$ . Thus, the “white-noise approximation” is meaningful when$$O(F\epsilon \sqrt{s})$$ , a quadratically weaker condition than the$$\epsilon \sqrt{s} \ll 1$$ requirement to maintain high fidelity. The bound applies if the circuit size satisfies$$\epsilon s\ll 1$$ , which corresponds to only$$s \ge \Omega (n\log (n))$$ logarithmic depth circuits, and if, additionally, the inverse error rate satisfies , which is needed to ensure errors are scrambled faster than$$\epsilon ^{-1} \ge {\tilde{\Omega }}(n)$$ F decays. The white-noise approximation is useful for salvaging the signal from a noisy quantum computation; for example, it was an underlying assumption in complexity-theoretic arguments that noisy random quantum circuits cannot be efficiently sampled classically, even when the fidelity is low. Our method is based on a map from second-moment quantities in random quantum circuits to expectation values of certain stochastic processes for which we compute upper and lower bounds. -
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