5 research outputs found
Quantum simulation of partially distinguishable boson sampling
Boson Sampling is the problem of sampling from the same output probability
distribution as a collection of indistinguishable single photons input into a
linear interferometer. It has been shown that, subject to certain computational
complexity conjectures, in general the problem is difficult to solve
classically, motivating optical experiments aimed at demonstrating quantum
computational "supremacy". There are a number of challenges faced by such
experiments, including the generation of indistinguishable single photons. We
provide a quantum circuit that simulates bosonic sampling with arbitrarily
distinguishable particles. This makes clear how distinguishabililty leads to
decoherence in the standard quantum circuit model, allowing insight to be
gained. At the heart of the circuit is the quantum Schur transform, which
follows from a representation theoretic approach to the physics of
distinguishable particles in first quantisation. The techniques are quite
general and have application beyond boson sampling.Comment: 25 pages, 4 figures, 2 algorithms, comments welcom
Classically simulating near-term partially-distinguishable and lossy boson sampling
Boson Sampling is the problem of sampling from the same distribution as
indistinguishable single photons at the output of a linear optical
interferometer. It is an example of a non-universal quantum computation which
is believed to be feasible in the near term and cannot be simulated on a
classical machine. Like all purported demonstrations of "quantum supremacy",
this motivates optimizing classical simulation schemes for a realistic model of
the problem, in this case Boson Sampling when the implementations experience
lost or distinguishable photons. Although current simulation schemes for
sufficiently imperfect boson sampling are classically efficient, in principle
the polynomial runtime can be infeasibly large. In this work, we develop a
scheme for classical simulation of Boson Sampling under uniform
distinguishability and loss, based on the idea of sampling from distributions
where at most k photons are indistinguishable. We show that asymptotically this
scheme can provide a polynomial improvement in the runtime compared to
classically simulating idealised Boson Sampling. More significantly, we show
that in the regime considered experimentally relevant, our approach gives an
substantial improvement in runtime over other classical simulation approaches.Comment: 15 pages, 5 figures, comments welcom
Compilation of a simple chemistry application to quantum error correction primitives
A number of exciting recent results have been seen in the field of quantum
error correction. These include initial demonstrations of error correction on
current quantum hardware, and resource estimates which improve understanding of
the requirements to run large-scale quantum algorithms for real-world
applications. In this work, we bridge the gap between these two developments by
performing careful estimation of the resources required to fault-tolerantly
perform quantum phase estimation (QPE) on a minimal chemical example.
Specifically, we describe a detailed compilation of the QPE circuit to lattice
surgery operations for the rotated surface code, for a hydrogen molecule in a
minimal basis set. We describe a number of optimisations at both the
algorithmic and error correction levels. We find that implementing even a
simple chemistry circuit requires 900 qubits and 2,300 quantum error correction
rounds, emphasising the need for improved error correction techniques
specifically targeting the early fault-tolerant regime.Comment: 22 pages, 23 figures, 1 table, source code available at
https://github.com/riverlane/h2_compilation