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Bulletin of the American Physical Society

Implementation of squeezing jump operators

Roland Cristopher F. Caballar, Gentaro Watanabe A, Sebastian Diehl, Harri M akel a

Published Mar 21, 2013• 0 citations
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Bosonic encodings of quantum information offer hardware-efficient, noise-biased approaches to quantum error correction relative to qubit register encodings. Implementations have focused in particular on error correction of stored, idle quantum information, whereas quantum algorithms are likely to desire high duty cycles of active control. Error-transparent operations are one way to preserve error rates during operations, but, to the best of our knowledge, only phase gates have so far been given an explicitly error-transparent formulation for binomial encodings. Here, we introduce the concept of 'parity nested' operations, and show how these operations can be designed to achieve continuous amplitude-mixing logical gates for binomial encodings that are fully error-transparent to the photon loss channel. For a binomial encoding that protects against l photon losses, the construction requires ⌊l/2⌋ + 1 orders of generalized squeezing in the parity nested operation to fully preserve this protection. We further show that error-transparency to all the correctable photon jumps, but not the no-jump errors, can be achieved with just a single order of squeezing. Finally, we comment on possible approaches to experimental realization of this concept.

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Reversing Open Quantum Dynamics via Continuous Petz Recovery Map

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One of the important issues in developing quantum technology is noise as quantum states are extremely sensitive to it. We propose a physical protocol which introduces reverse dynamics, in order to precisely control an open quantum system against noise. The reverse dynamics is realised by applying a well-controlled Hamiltonian and jump-operators. The control parameters for the Hamiltonian and jump operators are formulated by the Petz recovery map in continuous-time, from which we reverse the noisy quantum dynamics. The time-dependent jump operators can be implemented by considering strongly decaying ancillary qubits which interact with the system in a controlled manner. As a specific application, we demonstrate that our protocol efficiently suppresses only the noise part of dynamics thereby providing an effective unitary evolution of the quantum system.

•Apr 7, 2021•2 citations
Inspired by classical Markov Chain Monte Carlo (MCMC) methods, dissipative quantum algorithms are an emerging class of methods for preparing quantum states on a quantum computer. They operate by simulating a dissipative process governed by a mathematical operator known as the Lindbladian. The performance of these algorithms can be limited by the sequential implementation of the Lindbladian's constituent jump operators, which leads to high circuit depth. To address this issue, this work analyzes a parallelization scheme to implement jump operators simultaneously. We leverage the structure of geometric locality to show that individual jump operators remain spatially localized. This exponentially reduces the circuit depth per time step, resulting in an overall polynomial improvement. Numerical experiments demonstrate a 53x reduction in query depth for a 1D benchmark system of 100 qubits. The reduced circuit depth makes dissipative algorithms more practical for near-term quantum computing.
Bosonic encodings of quantum information offer hardware-efficient, noise-biased approaches to quantum error correction relative to qubit register encodings. Implementations have focused in particular on error correction of stored, idle quantum information, whereas quantum algorithms are likely to desire high duty cycles of active control. Error-transparent operations are one way to preserve error rates during operations, but, to the best of our knowledge, only phase gates have so far been given an explicitly error-transparent formulation for binomial encodings. Here, we introduce the concept of 'parity nested' operations, and show how these operations can be designed to achieve continuous amplitude-mixing logical gates for binomial encodings that are fully error-transparent to the photon loss channel. For a binomial encoding that protects against l photon losses, the construction requires ⌊l/2⌋ + 1 orders of generalized squeezing in the parity nested operation to fully preserve this protection. We further show that error-transparency to all the correctable photon jumps, but not the no-jump errors, can be achieved with just a single order of squeezing. Finally, we comment on possible approaches to experimental realization of this concept.
One of the important issues in developing quantum technology is noise as quantum states are extremely sensitive to it. We propose a physical protocol which introduces reverse dynamics, in order to precisely control an open quantum system against noise. The reverse dynamics is realised by applying a well-controlled Hamiltonian and jump-operators. The control parameters for the Hamiltonian and jump operators are formulated by the Petz recovery map in continuous-time, from which we reverse the noisy quantum dynamics. The time-dependent jump operators can be implemented by considering strongly decaying ancillary qubits which interact with the system in a controlled manner. As a specific application, we demonstrate that our protocol efficiently suppresses only the noise part of dynamics thereby providing an effective unitary evolution of the quantum system.