13 research outputs found
Mitigating photon loss in linear optical quantum circuits:classical postprocessing methods outperforming postselection
Photon loss rates set an effective upper limit on the size of computations that can be run on current linear optical quantum devices. We present a family of techniques to mitigate the effects of photon loss on both output probabilities and expectation values derived from noisy linear optical circuits composed of an input of photons, an -mode interferometer, and single photon detectors. Central to these techniques is the construction of objects called recycled probabilities. Recycled probabilities are constructed from output statistics affected by loss, and are designed to amplify the signal of the ideal (lossless) probabilities. Classical postprocessing techniques then take recycled probabilities as input and output a set of loss-mitigated probabilities, or expectation values. We provide analytical and numerical evidence that these methods can be applied, up to large sample sizes, to produce more accurate outputs than those obtained from postselection - which is currently the standard method of coping with photon loss when sampling from discrete variable linear optical quantum circuits. In contrast, we provide strong evidence that the popular zero noise extrapolation technique cannot improve on on the performance of postselection for any photon loss rate
Efficient approximate unitary t-designs from partially invertible universal sets and their application to quantum speedup
At its core a -design is a method for sampling from a set of unitaries in
a way which mimics sampling randomly from the Haar measure on the unitary
group, with applications across quantum information processing and physics. We
construct new families of quantum circuits on -qubits giving rise to
-approximate unitary -designs efficiently in
depth. These quantum circuits are based on a relaxation of technical
requirements in previous constructions. In particular, the construction of
circuits which give efficient approximate -designs by Brandao, Harrow, and
Horodecki (F.G.S.L Brandao, A.W Harrow, and M. Horodecki, Commun. Math. Phys.
(2016).) required choosing gates from ensembles which contained inverses for
all elements, and that the entries of the unitaries are algebraic. We reduce
these requirements, to sets that contain elements without inverses in the set,
and non-algebraic entries, which we dub partially invertible universal sets. We
then adapt this circuit construction to the framework of measurement based
quantum computation(MBQC) and give new explicit examples of -qubit graph
states with fixed assignments of measurements (graph gadgets) giving rise to
unitary -designs based on partially invertible universal sets, in a natural
way. We further show that these graph gadgets demonstrate a quantum speedup, up
to standard complexity theoretic conjectures. We provide numerical and
analytical evidence that almost any assignment of fixed measurement angles on
an -qubit cluster state give efficient -designs and demonstrate a quantum
speedup.Comment: 25 pages,7 figures. Comments are welcome. Some typos corrected in
newest version. new References added.Proofs unchanged. Results unchange
Mitigating errors by quantum verification and post-selection
Correcting errors due to noise in quantum circuits run on current and
near-term quantum hardware is essential for any convincing demonstration of
quantum advantage. Indeed, in many cases it has been shown that noise renders
quantum circuits efficiently classically simulable, thereby destroying any
quantum advantage potentially offered by an ideal (noiseless) implementation of
these circuits.
Although the technique of quantum error correction (QEC) allows to correct
these errors very accurately, QEC usually requires a large overhead of physical
qubits which is not reachable with currently available quantum hardware. This
has been the motivation behind the field of quantum error mitigation, which
aims at developing techniques to correct an important part of the errors in
quantum circuits, while also being compatible with current and near-term
quantum hardware.
In this work, we present a technique for quantum error mitigation which is
based on a technique from quantum verification, the so-called accreditation
protocol, together with post-selection. Our technique allows for correcting the
expectation value of an observable , which is the output of multiple runs of
noisy quantum circuits, where the noise in these circuits is at the level of
preparations, gates, and measurements. We discuss the sample complexity of our
procedure and provide rigorous guarantees of errors being mitigated under some
realistic assumptions on the noise. Our technique also allows for time
dependant behaviours, as we allow for the output states to be different between
different runs of the accreditation protocol. We validate our findings by
running our technique on currently available quantum hardware.Comment: 15 pages, 5 figures, 2 table
Solving graph problems with single-photons and linear optics
An important challenge for current and near-term quantum devices is finding
useful tasks that can be preformed on them. We first show how to efficiently
encode a bounded matrix into a linear optical circuit with
modes. We then apply this encoding to the case where is a matrix
containing information about a graph . We show that a photonic quantum
processor consisting of single-photon sources, a linear optical circuit
encoding , and single-photon detectors can solve a range of graph problems
including finding the number of perfect matchings of bipartite graphs,
computing permanental polynomials, determining whether two graphs are
isomorphic, and the -densest subgraph problem. We also propose
pre-processing methods to boost the probabilities of observing the relevant
detection events and thus improve performance. Finally, we present various
numerical simulations which validate our findings.Comment: 6 pages + 9 pages appendix. Comments Welcome
On Unitary <i>t</i>-Designs from Relaxed Seeds
The capacity to randomly pick a unitary across the whole unitary group is a
powerful tool across physics and quantum information. A unitary -design is
designed to tackle this challenge in an efficient way, yet constructions to
date rely on heavy constraints. In particular, they are composed of ensembles
of unitaries which, for technical reasons, must contain inverses and whose
entries are algebraic. In this work, we reduce the requirements for generating
an -approximate unitary -design. To do so, we first construct a
specific -qubit random quantum circuit composed of a sequence of, randomly
chosen, 2-qubit gates, chosen from a set of unitaries which is approximately
universal on , yet need not contain unitaries and their inverses, nor are
in general composed of unitaries whose entries are algebraic; dubbed
seed. We then show that this relaxed seed, when used as a basis for our
construction, gives rise to an -approximate unitary -design
efficiently, where the depth of our random circuit scales as , thereby overcoming the two requirements which limited
previous constructions.
We suspect the result found here is not optimal, and can be improved.
Particularly because the number of gates in the relaxed seeds introduced here
grows with and . We conjecture that constant sized seeds such as those
in ( Brand\~ao, Harrow, and Horodecki; Commun. Math. Phys. (2016) 346: 397) are
sufficient.Comment: Typos corrected. Readability improved. Results unchanged. Proofs
unchange
Perceval: A Software Platform for Discrete Variable Photonic Quantum Computing
We introduce Perceval, an evolutive open-source software platform for
simulating and interfacing with discrete variable photonic quantum computers,
and describe its main features and components. Its Python front-end allows
photonic circuits to be composed from basic photonic building blocks like
photon sources, beam splitters, phase shifters and detectors. A variety of
computational back-ends are available and optimised for different use-cases.
These use state-of-the-art simulation techniques covering both weak simulation,
or sampling, and strong simulation. We give examples of Perceval in action by
reproducing a variety of photonic experiments and simulating photonic
implementations of a range of quantum algorithms, from Grover's and Shor's to
examples of quantum machine learning. Perceval is intended to be a useful
toolkit both for experimentalists wishing to easily model, design, simulate, or
optimise a discrete variable photonic experiment, and for theoreticians wishing
to design algorithms and applications for discrete-variable photonic quantum
computing platforms
Aléatoire pour le traitement de l'information quantique
This thesis is focused on the generation and understanding of particular kinds of quantum randomness. Randomness is useful for many tasks in physics and information processing, from randomized benchmarking , to black hole physics , as well demonstrating a so-called quantum speedup , and many other applications. On the one hand we explore how to generate a particular form of random evolution known as a t-design. On the other we show how this can also give instances for quantum speedup - where classical computers cannot simulate the randomness efficiently. We also show that this is still possible in noisy realistic settings. More specifically, this thesis is centered around three main topics. The first of these being the generation of epsilon-approximate unitary t-designs. In this direction, we first show that non-adaptive, fixed measurements on a graph state composed of poly(n,t,log(1/epsilon)) qubits, and with a regular structure (that of a brickwork state) effectively give rise to a random unitary ensemble which is a epsilon-approximate t-design. This work is presented in Chapter 3. Before this work, it was known that non-adaptive fixed XY measurements on a graph state give rise to unitary t-designs , however the graph states used there were of complicated structure and were therefore not natural candidates for measurement based quantum computing (MBQC), and the circuits to make them were complicated. The novelty in our work is showing that t-designs can be generated by fixed, non-adaptive measurements on graph states whose underlying graphs are regular 2D lattices. These graph states are universal resources for MBQC. Therefore, our result allows the natural integration of unitary t-designs, which provide a notion of quantum pseudorandomness which is very useful in quantum algorithms, into quantum algorithms running in MBQC. Moreover, in the circuit picture this construction for t-designs may be viewed as a constant depth quantum circuit, albeit with a polynomial number of ancillas. We then provide new constructions of epsilon-approximate unitary t-designs both in the circuit model and in MBQC which are based on a relaxation of technical requirements in previous constructions. These constructions are found in Chapters 4 and 5.Cette thèse est basée sur la génération et la compréhension de types particuliers des ensembles unitaires aleatoires. Ces ensembles est utile pour de nombreuses applications de physique et de l’Information Quantique, comme le benchmarking aléatoire, la physique des trous noirs, ainsi qu’à la démonstration de ce que l’on appelle un "quantum speedup" etc. D'une part, nous explorons comment générer une forme particulière d'évolution aléatoire appelée epsilon-approximateunitary t-designs . D'autre part, nous montrons comment cela peut également donner des exemples de quantum speedup, où les ordinateurs classiques ne peuvent pas simuler en temps polynomiale le caractère aléatoire. Nous montrons également que cela est toujours possible dans des environnements bruyants et réalistes
Unitary -designs from seeds
In this work we reduce the requirements for generating -designs, an important tool for randomisation with applications across quantum information and physics. We show that random quantum circuits with support over families of finite sets of unitaries which are approximately universal in (we call such sets ), converge towards approximate unitary -designs efficiently in depth, where is the number of inputs of the random quantum circuit, and is the order of the design. We show this convergence for seeds which are relaxed in the sense that every unitary matrix in the seed need not have an inverse in the seed, nor be composed entirely of algebraic entries in general, two requirements which have restricited previous constructions. We suspect the result found here is not optimal, and can be improved. Particularly because the number of gates in the relaxed seeds introduced here grows with and . We conjecture that constant sized seeds such as those in (Brand\~ao, Harrow, and Horodecki, Commun. Math. Phys. 2016) are sufficient
Perceval: A Software Platform for Discrete Variable Photonic Quantum Computing
We introduce , an open-source software platform for simulating and interfacing with discrete-variable photonic quantum computers, and describe its main features and components. Its Python front-end allows photonic circuits to be composed from basic photonic building blocks like photon sources, beam splitters, phase-shifters and detectors. A variety of computational back-ends are available and optimised for different use-cases. These use state-of-the-art simulation techniques covering both weak simulation, or sampling, and strong simulation. We give examples of in action by reproducing a variety of photonic experiments and simulating photonic implementations of a range of quantum algorithms, from Grover's and Shor's to examples of quantum machine learning. is intended to be a useful toolkit for experimentalists wishing to easily model, design, simulate, or optimise a discrete-variable photonic experiment, for theoreticians wishing to design algorithms and applications for discrete-variable photonic quantum computing platforms, and for application designers wishing to evaluate algorithms on available state-of-the-art photonic quantum computers