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NASA NTRSDate not supplied

Logical shadow tomography: Efficient estimation of error-mitigated observables

We introduce a technique to estimate error-mitigated expectation values on noisy quantum computers. Our technique performs shadow tomography on a logical state to produce a memory-efficient classical reconstruction of the noisy density matrix. Using efficient classical post-processing, one can mitigate errors by projecting into the codespace as in subspace expansion and taking powers of the density matrix as in virtual distillation. Relative to subspace expansion which requires Ω (2^((n-1)k) samples to estimate a Pauli observable with an [[n; k]] stabilizer code, our technique requires only Ө(2^k) samples. Relative to virtual distillation, our technique can compute powers of the density matrix without implementing additional copies of quantum states the quantum computer. We present numerical results using logical states encoded with up to sixty physical qubits and show fast convergence to error-free expectation values with only 10^5 samples under 1% depolarizing noise.

quantum computing↗

NASA NTRSDate not supplied

Logical Shadow Tomography: Efficient Estimation of Error-mitigated Observables

In near-term quantum applications, reducing errors and improving device reliability is an essential task. Towards these ends, various techniques have been introduced in recent literature, collectively referred to as quantum error mitigation techniques, for reducing errors in pre-fault-tolerant devices. Here, we introduce logical shadow tomography as a versatile error mitigation method. Our technique uses a stabilizer code to encode information in a logical state. Instead of doing active error correction, quantum states will be measured at the end of computation via shadow tomography and non-logical errors are projected out in the classical post-processing. Relative to quantum subspace expansion which requires O(2(M-1)L) experiments to estimate an logical Pauli observable encoded by an [[M, L, d]] code, our technique only requires 2L experiments, an important practical reduction in resources.

Hong-Ye Hu↗

NASA NTRSDate not supplied

Hardware-Efficient Quantum Optimization Layered Algorithms and Experiments

Quantum optimization algorithms, such as QAOA, that implement parametrized stochastic optimization solvers attempt to identify low-energy solutions of Ising systems by exploiting available quantum effects in noisy-intermediate scale machines. Engineering a well-performing parametrized quantum optimization circuit is indeed an exercise in balancing the trade-off between expressivity and implementation complexity. We show that, for MaxCut QAOA circuits defined on native hardware topology (Rigetti’s Aspen Quantum Processors), error-mitigation techniques recover simulated features of the noiseless theory. Moreover, we explore a design space for QAOA-like ansatze that perform well in theory as well as in hardware for fully-connected problems. We also discuss how efficient coherence and entanglement detection methods that could be coupled with quantum optimization experiments require only linear overhead in benchmarking time.

quantum computing↗