Abstract
The required set of operations for universal continuous-variable quantum computation can be divided into two primary categories: Gaussian and non-Gaussian operations. Furthermore, any Gaussian operation can be decomposed as a sequence of phase-space displacements and symplectic transformations. Although Gaussian operations are ubiquitous in quantum optics, their experimental realizations generally are approximations of the ideal Gaussian unitaries. In this work, we study different performance criteria to analyze how well these experimental approximations simulate the ideal Gaussian unitaries. In particular, we find that none of these experimental approximations converge uniformly to the ideal Gaussian unitaries. However, convergence occurs in the strong sense, or if the discrimination strategy is energy bounded, then the convergence is uniform in the Shirokov-Winter energy-constrained diamond norm and we give explicit bounds in this latter case. We indicate how these energy-constrained bounds can be used for experimental implementations of these Gaussian unitaries in order to achieve any desired accuracy.
Highlights
Quantum computers use quantum properties such as superposition of quantum states and entanglement for information processing and computational tasks [1]
One of the notions of universal quantum computation consists of the manipulation of qubits encoded in discrete quantum systems and the application of a universal set of quantum operations on these qubits [1]
Another way to implement discrete-variable (DV) quantum computation is to encode a finite amount of quantum information into a continuous-variable (CV) system [2,3,4]. This approach is appealing given that already existing advanced optical technologies can be used for state preparation, manipulation of states, and measurement for the required quantum computational tasks [5]
Summary
Quantum computers use quantum properties such as superposition of quantum states and entanglement for information processing and computational tasks [1]. We study uniform convergence over the energy-bounded quantum states of some experimental approximations of both an ideal single-mode squeezing operation and a SUM gate, by considering several experimentally relevant input quantum states. These Gaussian unitaries are key elements for CV quantum computation [6], CV quantum error correction [34,35,36], CV quantum teleportation [37], improving the sensitivity of an interferometer in the context of quantum metrological tasks [38], for generating a quantum nondemolition interaction. For additional details see Ref. [60]
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