This content will become publicly available on January 1, 2023
 Award ID(s):
 1818914
 Publication Date:
 NSFPAR ID:
 10339353
 Journal Name:
 ArXivorg
 ISSN:
 23318422
 Sponsoring Org:
 National Science Foundation
More Like this

Quantum errorcorrecting codes can be used to protect qubits involved in quantum computation. This requires that logical operators acting on protected qubits be translated to physical operators (circuits) acting on physical quantum states. We propose a mathematical framework for synthesizing physical circuits that implement logical Clifford operators for stabilizer codes. Circuit synthesis is enabled by representing the desired physical Clifford operator in CN ×N as a 2m × 2m binary sym plectic matrix, where N = 2m. We show that for an [m, m − k] stabilizer code every logical Clifford operator has 2k(k+1)/2 symplectic solutions, and we enumerate them efficiently using symplectic transvections. The desired circuits are then obtained by writing each of the solutions as a product of elementary symplectic matrices. For a given operator, our assembly of all of its physical realizations enables optimization over them with respect to a suitable metric. Our method of circuit synthesis can be applied to any stabilizer code, and this paper provides a proof of concept synthesis of universal Clifford gates for the well known [6, 4, 2] code. Programs implementing our algorithms can be found at https://github.com/nrenga/symplecticarxiv18a.

Abstract To achieve universal quantum computation via general faulttolerant schemes, stabilizer operations must be supplemented with other nonstabilizer quantum resources. Motivated by this necessity, we develop a resource theory for magic quantum channels to characterize and quantify the quantum ‘magic’ or nonstabilizerness of noisy quantum circuits. For qudit quantum computing with odd dimension
d , it is known that quantum states with nonnegative Wigner function can be efficiently simulated classically. First, inspired by this observation, we introduce a resource theory based on completely positiveWignerpreserving quantum operations as free operations, and we show that they can be efficiently simulated via a classical algorithm. Second, we introduce two efficiently computable magic measures for quantum channels, called the mana and thauma of a quantum channel. As applications, we show that these measures not only provide fundamental limits on the distillable magic of quantum channels, but they also lead to lower bounds for the task of synthesizing nonClifford gates. Third, we propose a classical algorithm for simulating noisy quantum circuits, whose sample complexity can be quantified by the mana of a quantum channel. We further show that this algorithm can outperform another approach for simulating noisy quantum circuits, based on channel robustness. Finally, we explore themore » 
Quantum chemistry is a promising application for noisy intermediatescale quantum (NISQ) devices. However, quantum computers have thus far not succeeded in providing solutions to problems of real scientific significance, with algorithmic advances being necessary to fully utilise even the modest NISQ machines available today. We discuss a method of ground state energy estimation predicated on a partitioning the molecular Hamiltonian into two parts: one that is noncontextual and can be solved classically, supplemented by a contextual component that yields quantum corrections obtained via a Variational Quantum Eigensolver (VQE) routine. This approach has been termed Contextual Subspace VQE (CSVQE), but there are obstacles to overcome before it can be deployed on NISQ devices. The problem we address here is that of the ansatz  a parametrized quantum state over which we optimize during VQE. It is not initially clear how a splitting of the Hamiltonian should be reflected in our CSVQE ansätze. We propose a 'noncontextual projection' approach that is illuminated by a reformulation of CSVQE in the stabilizer formalism. This defines an ansatz restriction from the full electronic structure problem to the contextual subspace and facilitates an implementation of CSVQE that may be deployed on NISQ devices. We validate themore »

Abstract Variational quantum circuits (VQCs) have shown great potential in nearterm applications. However, the discriminative power of a VQC, in connection to its circuit architecture and depth, is not understood. To unleash the genuine discriminative power of a VQC, we propose a VQC system with the optimal classical postprocessing—maximumlikelihood estimation on measuring all VQC output qubits. Via extensive numerical simulations, we find that the error of VQC quantum data classification typically decays exponentially with the circuit depth, when the VQC architecture is extensive—the number of gates does not shrink with the circuit depth. This fast error suppression ends at the saturation towards the ultimate Helstrom limit of quantum state discrimination. On the other hand, nonextensive VQCs such as quantum convolutional neural networks are suboptimal and fail to achieve the Helstrom limit, demonstrating a tradeoff between ansatz complexity and classification performance in general. To achieve the best performance for a given VQC, the optimal classical postprocessing is crucial even for a binary classification problem. To simplify VQCs for nearterm implementations, we find that utilizing the symmetry of the input properly can improve the performance, while oversimplification can lead to degradation.

Quantum simulations of electronic structure with a transformed Hamiltonian that includes some electron correlation effects are demonstrated. The transcorrelated Hamiltonian used in this work is efficiently constructed classically, at polynomial cost, by an approximate similarity transformation with an explicitly correlated twobody unitary operator. This Hamiltonian is Hermitian, includes no more than twoparticle interactions, and is free of electron–electron singularities. We investigate the effect of such a transformed Hamiltonian on the accuracy and computational cost of quantum simulations by focusing on a widely used solver for the Schrödinger equation, namely the variational quantum eigensolver method, based on the unitary coupled cluster with singles and doubles (qUCCSD) Ansatz. Nevertheless, the formalism presented here translates straightforwardly to other quantum algorithms for chemistry. Our results demonstrate that a transcorrelated Hamiltonian, paired with extremely compact bases, produces explicitly correlated energies comparable to those from much larger bases. For the chemical species studied here, explicitly correlated energies based on an underlying 631G basis had ccpVTZ quality. The use of the very compact transcorrelated Hamiltonian reduces the number of CNOT gates required to achieve ccpVTZ quality by up to two orders of magnitude, and the number of qubits by a factor of three.