38 research outputs found
Recommended from our members
The power of restricted quantum computational models
Restricted models of quantum computation are ones that have less power than a universal quantum computer. We studied the consequences of removing particular properties from a universal quantum computer to discover whether those resources were important.In the first part of the thesis we studied universal quantum computers which are implemented using Clifford gates, adaptive measurements, and magic states. The Gottesman–Knill theorem shows that circuits in this form which do not use magic states can be simulated by a classical computer. We extended this result to show that all circuits in this form can be partially simulated; the same computation can be implemented using a smaller quantum computer with the assistance of some polynomial time classical computation. We also identified a subclass of these computations that can be shown to not be entirely classically simulated by any method, given certain complexity theoretic assumptions are true.In the next part of the thesis we examine the role of entanglement in noisy quantum computations. Entanglement is necessary for noiseless quantum computers to have any quantum advantage, but it is not known whether the same is true for mixed state quantum computers. We show that entanglement, unexpectedly, does play a crucial role in the most well known mixed state computer: the one clean qubit model.Finally, we investigate how closely classical simulation is related to another idea of classicality.This notion captures how easily the final state of a computation can be learnt, given samples of measurements from it. We find an extra condition under which a circuit that is classically simulable is also efficiently learnable
Efficient Learning of Non-Interacting Fermion Distributions
We give an efficient classical algorithm that recovers the distribution of a
non-interacting fermion state over the computational basis. For a system of
non-interacting fermions and modes, we show that samples and time are
sufficient to learn the original distribution to total variation distance
with probability . Our algorithm empirically
estimates the one- and two-mode correlations and uses them to reconstruct a
succinct description of the entire distribution efficiently.Comment: 7 page
Learning the tensor network model of a quantum state using a few single-qubit measurements
The constantly increasing dimensionality of artificial quantum systems
demands for highly efficient methods for their characterization and
benchmarking. Conventional quantum tomography fails for larger systems due to
the exponential growth of the required number of measurements. The conceptual
solution for this dimensionality curse relies on a simple idea - a complete
description of a quantum state is excessive and can be discarded in favor of
experimentally accessible information about the system. The probably
approximately correct (PAC) learning theory has been recently successfully
applied to a problem of building accurate predictors for the measurement
outcomes using a dataset which scales only linearly with the number of qubits.
Here we present a constructive and numerically efficient protocol which learns
a tensor network model of an unknown quantum system. We discuss the limitations
and the scalability of the proposed method.Comment: 10 pages, 11 figure
A survey on the complexity of learning quantum states
We survey various recent results that rigorously study the complexity of
learning quantum states. These include progress on quantum tomography, learning
physical quantum states, alternate learning models to tomography and learning
classical functions encoded as quantum states. We highlight how these results
are paving the way for a highly successful theory with a range of exciting open
questions. To this end, we distill 25 open questions from these results.Comment: Invited article by Nature Review Physics. 39 pages, 6 figure
Experimental learning of quantum states
The number of parameters describing a quantum state is well known to grow exponentially with the number of particles. This scaling limits our ability to characterize and simulate the evolution of arbitrary states to systems, with no more than a few qubits. However, from a computational learning theory perspective, it can be shown that quantum states can be approximately learned using a number of measurements growing linearly with the number of qubits. Here, we experimentally demonstrate this linear scaling in optical systems with up to 6 qubits. Our results highlight the power of the computational learning theory to investigate quantum information, provide the first experimental demonstration that quantum states can be "probably approximately learned" with access to a number of copies of the state that scales linearly with the number of qubits, and pave the way to probing quantum states at new, larger scales