17 research outputs found
Numerical circuit synthesis and compilation for multi-state preparation
Near-term quantum computers have significant error rates and short coherence
times, so compilation of circuits to be as short as possible is essential. Two
types of compilation problems are typically considered: circuits to prepare a
given state from a fixed input state, called "state preparation"; and circuits
to implement a given unitary operation, for example by "unitary synthesis". In
this paper we solve a more general problem: the transformation of a set of
states to another set of states, which we call "multi-state preparation".
State preparation and unitary synthesis are special cases; for state
preparation, , while for unitary synthesis, is the dimension of the
full Hilbert space. We generate and optimize circuits for multi-state
preparation numerically. In cases where a top-down approach based on matrix
decompositions is also possible, our method finds circuits with substantially
(up to 40%) fewer two-qubit gates. We discuss possible applications, including
efficient preparation of macroscopic superposition ("cat") states and synthesis
of quantum channels.Comment: v2: Added to discussion in Sections IIA and VIB; v1: 10 pages, 2
figure
Option Pricing using Quantum Computers
We present a methodology to price options and portfolios of options on a
gate-based quantum computer using amplitude estimation, an algorithm which
provides a quadratic speedup compared to classical Monte Carlo methods. The
options that we cover include vanilla options, multi-asset options and
path-dependent options such as barrier options. We put an emphasis on the
implementation of the quantum circuits required to build the input states and
operators needed by amplitude estimation to price the different option types.
Additionally, we show simulation results to highlight how the circuits that we
implement price the different option contracts. Finally, we examine the
performance of option pricing circuits on quantum hardware using the IBM Q
Tokyo quantum device. We employ a simple, yet effective, error mitigation
scheme that allows us to significantly reduce the errors arising from noisy
two-qubit gates.Comment: Fixed a typo. This article has been accepted in Quantu
Machine learning logical gates for quantum error correction
Quantum error correcting codes protect quantum computation from errors caused
by decoherence and other noise. Here we study the problem of designing logical
operations for quantum error correcting codes. We present an automated
procedure which generates logical operations given known encoding and
correcting procedures. Our technique is to use variational circuits for
learning both the logical gates and the physical operations implementing them.
This procedure can be implemented on near-term quantum computers via quantum
process tomography. It enables automatic discovery of logical gates from
analytically designed error correcting codes and can be extended to error
correcting codes found by numerical optimizations. We test the procedure by
simulation on classical computers on small quantum codes of four qubits to
fifteen qubits and show that it finds most logical gates known in the current
literature. Additionally, it generates logical gates not found in the current
literature for the [[5,1,2]] code, the [[6,3,2]] code, and the [[8,3,2]] code.Comment: 17 page
Quantum Circuits for Sparse Isometries
We consider the task of breaking down a quantum computation given as an
isometry into C-NOTs and single-qubit gates, while keeping the number of C-NOT
gates small. Although several decompositions are known for general isometries,
here we focus on a method based on Householder reflections that adapts well in
the case of sparse isometries. We show how to use this method to decompose an
arbitrary isometry before illustrating that the method can lead to significant
improvements in the case of sparse isometries. We also discuss the classical
complexity of this method and illustrate its effectiveness in the case of
sparse state preparation by applying it to randomly chosen sparse states.Comment: 12+3 pages, 1 figure. v2: minor changes. Methods introduced here have
now been implemented in UniversalQCompiler, see
https://github.com/Q-Compiler/UniversalQCompiler . Raw data used in the
figure is available in the ancillary fil
Generation of Photonic Matrix Product States with a Rydberg-Blockaded Atomic Array
In this work, we show how one can deterministically generate photonic matrix
product states with high bond and physical dimensions with an atomic array if
one has access to a Rydberg-blockade mechanism. We develop both a quantum gate
and an optimal control approach to universally control the system and analyze
the photon retrieval efficiency of atomic arrays. Comprehensive modeling of the
system shows that our scheme is capable of generating a large number of
entangled photons. We further develop a multi-port photon emission approach
that can efficiently distribute entangled photons into free space in several
directions, which can become a useful tool in future quantum networks.Comment: 21 pages, 12 figure
Quantum Sensor Network Algorithms for Transmitter Localization
A quantum sensor (QS) is able to measure various physical phenomena with
extreme sensitivity. QSs have been used in several applications such as atomic
interferometers, but few applications of a quantum sensor network (QSN) have
been proposed or developed. We look at a natural application of QSN --
localization of an event (in particular, of a wireless signal transmitter). In
this paper, we develop effective quantum-based techniques for the localization
of a transmitter using a QSN. Our approaches pose the localization problem as a
well-studied quantum state discrimination (QSD) problem and address the
challenges in its application to the localization problem. In particular, a
quantum state discrimination solution can suffer from a high probability of
error, especially when the number of states (i.e., the number of potential
transmitter locations in our case) can be high. We address this challenge by
developing a two-level localization approach, which localizes the transmitter
at a coarser granularity in the first level, and then, in a finer granularity
in the second level. We address the additional challenge of the impracticality
of general measurements by developing new schemes that replace the QSD's
measurement operator with a trained parameterized hybrid quantum-classical
circuit. Our evaluation results using a custom-built simulator show that our
best scheme is able to achieve meter-level (1-5m) localization accuracy; in the
case of discrete locations, it achieves near-perfect (99-100\%) classification
accuracy.Comment: 11 pages, 10 figure