7,838 research outputs found
Characterizing the performance of continuous-variable Gaussian quantum gates
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.Comment: v3: 26 pages, 10 figures, final version accepted for publication in
Physical Review Researc
A new bound of the β2[0, T]-induced norm and applications to model reduction
We present a simple bound on the finite horizon β2/[0, T]-induced norm of a linear time-invariant (LTI), not necessarily stable system which can be efficiently computed by calculating the ββ norm of a shifted version of the original operator. As an application, we show how to use this bound to perform model reduction of unstable systems over a finite horizon. The technique is illustrated with a non-trivial physical example relevant to the appearance of time-irreversible phenomena in statistical physics
Estimating operator norms using covering nets
We present several polynomial- and quasipolynomial-time approximation schemes
for a large class of generalized operator norms. Special cases include the
norm of matrices for , the support function of the set of
separable quantum states, finding the least noisy output of
entanglement-breaking quantum channels, and approximating the injective tensor
norm for a map between two Banach spaces whose factorization norm through
is bounded.
These reproduce and in some cases improve upon the performance of previous
algorithms by Brand\~ao-Christandl-Yard and followup work, which were based on
the Sum-of-Squares hierarchy and whose analysis used techniques from quantum
information such as the monogamy principle of entanglement. Our algorithms, by
contrast, are based on brute force enumeration over carefully chosen covering
nets. These have the advantage of using less memory, having much simpler proofs
and giving new geometric insights into the problem. Net-based algorithms for
similar problems were also presented by Shi-Wu and Barak-Kelner-Steurer, but in
each case with a run-time that is exponential in the rank of some matrix. We
achieve polynomial or quasipolynomial runtimes by using the much smaller nets
that exist in spaces. This principle has been used in learning theory,
where it is known as Maurey's empirical method.Comment: 24 page
Simulating Quantum Dynamics On A Quantum Computer
We present efficient quantum algorithms for simulating time-dependent
Hamiltonian evolution of general input states using an oracular model of a
quantum computer. Our algorithms use either constant or adaptively chosen time
steps and are significant because they are the first to have time-complexities
that are comparable to the best known methods for simulating time-independent
Hamiltonian evolution, given appropriate smoothness criteria on the Hamiltonian
are satisfied. We provide a thorough cost analysis of these algorithms that
considers discretizion errors in both the time and the representation of the
Hamiltonian. In addition, we provide the first upper bounds for the error in
Lie-Trotter-Suzuki approximations to unitary evolution operators, that use
adaptively chosen time steps.Comment: Paper modified from previous version to enhance clarity. Comments are
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