20 research outputs found
Qubit-efficient encoding schemes for binary optimisation problems
We propose and analyze a set of variational quantum algorithms for solving
quadratic unconstrained binary optimization problems where a problem consisting
of classical variables can be implemented on
number of qubits. The underlying encoding scheme allows for a systematic
increase in correlations among the classical variables captured by a
variational quantum state by progressively increasing the number of qubits
involved. We first examine the simplest limit where all correlations are
neglected, i.e. when the quantum state can only describe statistically
independent classical variables. We apply this minimal encoding to find
approximate solutions of a general problem instance comprised of 64 classical
variables using 7 qubits. Next, we show how two-body correlations between the
classical variables can be incorporated in the variational quantum state and
how it can improve the quality of the approximate solutions. We give an example
by solving a 42-variable Max-Cut problem using only 8 qubits where we exploit
the specific topology of the problem. We analyze whether these cases can be
optimized efficiently given the limited resources available in state-of-the-art
quantum platforms. Lastly, we present the general framework for extending the
expressibility of the probability distribution to any multi-body correlations.Comment: 9 pages of main text + 6 figures. Comments are welcom
Quantum supremacy in driven quantum many-body systems
A crucial milestone in the field of quantum simulation and computation is to
demonstrate that a quantum device can compute certain tasks that are impossible
to reproduce by a classical computer with any reasonable resources. Such a
demonstration is referred to as quantum supremacy. One of the most important
questions is to identify setups that exhibit quantum supremacy and can be
implemented with current quantum technology. The two standard candidates are
boson sampling and random quantum circuits. Here, we show that quantum
supremacy can be obtained in generic periodically-driven quantum many-body
systems. Our analysis is based on the eigenstate thermalization hypothesis and
strongly-held conjectures in complexity theory. To illustrate our work, We give
examples of simple disordered Ising chains driven by global magnetic fields and
Bose-Hubbard chains with modulated hoppings. Our proposal opens the way for a
large class of quantum platforms to demonstrate and benchmark quantum
supremacy
Autonomous quantum error correction of Gottesman-Kitaev-Preskill states
The Gottesman-Kitaev-Preskill (GKP) code encodes a logical qubit into a
bosonic system with resilience against single-photon loss, the predominant
error in most bosonic systems. Here we present experimental results
demonstrating quantum error correction of GKP states based on reservoir
engineering of a superconducting device. Error correction is made autonomous
through an unconditional reset of an auxiliary transmon qubit. The lifetime of
the logical qubit is shown to be increased from quantum error correction,
therefore reaching the point at which more errors are corrected than generated.Comment: 6 pages, 3 figures + 26 pages, 12 figure