435 research outputs found
Applying Grover's algorithm to AES: quantum resource estimates
We present quantum circuits to implement an exhaustive key search for the
Advanced Encryption Standard (AES) and analyze the quantum resources required
to carry out such an attack. We consider the overall circuit size, the number
of qubits, and the circuit depth as measures for the cost of the presented
quantum algorithms. Throughout, we focus on Clifford gates as the
underlying fault-tolerant logical quantum gate set. In particular, for all
three variants of AES (key size 128, 192, and 256 bit) that are standardized in
FIPS-PUB 197, we establish precise bounds for the number of qubits and the
number of elementary logical quantum gates that are needed to implement
Grover's quantum algorithm to extract the key from a small number of AES
plaintext-ciphertext pairs.Comment: 13 pages, 3 figures, 5 tables; to appear in: Proceedings of the 7th
International Conference on Post-Quantum Cryptography (PQCrypto 2016
Hybrid quantum computing with ancillas
In the quest to build a practical quantum computer, it is important to use
efficient schemes for enacting the elementary quantum operations from which
quantum computer programs are constructed. The opposing requirements of
well-protected quantum data and fast quantum operations must be balanced to
maintain the integrity of the quantum information throughout the computation.
One important approach to quantum operations is to use an extra quantum system
- an ancilla - to interact with the quantum data register. Ancillas can mediate
interactions between separated quantum registers, and by using fresh ancillas
for each quantum operation, data integrity can be preserved for longer. This
review provides an overview of the basic concepts of the gate model quantum
computer architecture, including the different possible forms of information
encodings - from base two up to continuous variables - and a more detailed
description of how the main types of ancilla-mediated quantum operations
provide efficient quantum gates.Comment: Review paper. An introduction to quantum computation with qudits and
continuous variables, and a review of ancilla-based gate method
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
Fault-Tolerant Measurement-Based Quantum Computing with Continuous-Variable Cluster States
A long-standing open question about Gaussian continuous-variable cluster
states is whether they enable fault-tolerant measurement-based quantum
computation. The answer is yes. Initial squeezing in the cluster above a
threshold value of 20.5 dB ensures that errors from finite squeezing acting on
encoded qubits are below the fault-tolerance threshold of known qubit-based
error-correcting codes. By concatenating with one of these codes and using
ancilla-based error correction, fault-tolerant measurement-based quantum
computation of theoretically indefinite length is possible with finitely
squeezed cluster states.Comment: (v3) consistent with published version, more accessible for general
audience; (v2) condensed presentation, added references on GKP state
generation and a comparison of currently achievable squeezing to the
threshold; (v1) 13 pages, a few figure
Layered architecture for quantum computing
We develop a layered quantum computer architecture, which is a systematic
framework for tackling the individual challenges of developing a quantum
computer while constructing a cohesive device design. We discuss many of the
prominent techniques for implementing circuit-model quantum computing and
introduce several new methods, with an emphasis on employing surface code
quantum error correction. In doing so, we propose a new quantum computer
architecture based on optical control of quantum dots. The timescales of
physical hardware operations and logical, error-corrected quantum gates differ
by several orders of magnitude. By dividing functionality into layers, we can
design and analyze subsystems independently, demonstrating the value of our
layered architectural approach. Using this concrete hardware platform, we
provide resource analysis for executing fault-tolerant quantum algorithms for
integer factoring and quantum simulation, finding that the quantum dot
architecture we study could solve such problems on the timescale of days.Comment: 27 pages, 20 figure
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