17 research outputs found

    Numerical circuit synthesis and compilation for multi-state preparation

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    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 mm states to another set of mm states, which we call "multi-state preparation". State preparation and unitary synthesis are special cases; for state preparation, m=1m=1, while for unitary synthesis, mm 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

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    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

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    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

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    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

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    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

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    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
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