393 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
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
Concrete resource analysis of the quantum linear system algorithm used to compute the electromagnetic scattering cross section of a 2D target
We provide a detailed estimate for the logical resource requirements of the
quantum linear system algorithm (QLSA) [Phys. Rev. Lett. 103, 150502 (2009)]
including the recently described elaborations [Phys. Rev. Lett. 110, 250504
(2013)]. Our resource estimates are based on the standard quantum-circuit model
of quantum computation; they comprise circuit width, circuit depth, the number
of qubits and ancilla qubits employed, and the overall number of elementary
quantum gate operations as well as more specific gate counts for each
elementary fault-tolerant gate from the standard set {X, Y, Z, H, S, T, CNOT}.
To perform these estimates, we used an approach that combines manual analysis
with automated estimates generated via the Quipper quantum programming language
and compiler. Our estimates pertain to the example problem size N=332,020,680
beyond which, according to a crude big-O complexity comparison, QLSA is
expected to run faster than the best known classical linear-system solving
algorithm. For this problem size, a desired calculation accuracy 0.01 requires
an approximate circuit width 340 and circuit depth of order if oracle
costs are excluded, and a circuit width and depth of order and
, respectively, if oracle costs are included, indicating that the
commonly ignored oracle resources are considerable. In addition to providing
detailed logical resource estimates, it is also the purpose of this paper to
demonstrate explicitly how these impressively large numbers arise with an
actual circuit implementation of a quantum algorithm. While our estimates may
prove to be conservative as more efficient advanced quantum-computation
techniques are developed, they nevertheless provide a valid baseline for
research targeting a reduction of the resource requirements, implying that a
reduction by many orders of magnitude is necessary for the algorithm to become
practical.Comment: 37 pages, 40 figure
Measurement-free fault-tolerant quantum error correction in near-term devices
Logical qubits can be protected from decoherence by performing QEC cycles
repeatedly. Algorithms for fault-tolerant QEC must be compiled to the specific
hardware platform under consideration in order to practically realize a quantum
memory that operates for in principle arbitrary long times. All circuit
components must be assumed as noisy unless specific assumptions about the form
of the noise are made. Modern QEC schemes are challenging to implement
experimentally in physical architectures where in-sequence measurements and
feed-forward of classical information cannot be reliably executed fast enough
or even at all. Here we provide a novel scheme to perform QEC cycles without
the need of measuring qubits that is fully fault-tolerant with respect to all
components used in the circuit. Our scheme can be used for any low-distance CSS
code since its only requirement towards the underlying code is a transversal
CNOT gate. Similarly to Steane-type EC, we coherently copy errors to a logical
auxiliary qubit but then apply a coherent feedback operation from the auxiliary
system to the logical data qubit. The logical auxiliary qubit is prepared
fault-tolerantly without measurements, too. We benchmark logical failure rates
of the scheme in comparison to a flag-qubit based EC cycle. We map out a
parameter region where our scheme is feasible and estimate physical error rates
necessary to achieve the break-even point of beneficial QEC with our scheme. We
outline how our scheme could be implemented in ion traps and with neutral atoms
in a tweezer array. For recently demonstrated capabilities of atom shuttling
and native multi-atom Rydberg gates, we achieve moderate circuit depths and
beneficial performance of our scheme while not breaking fault tolerance. These
results thereby enable practical fault-tolerant QEC in hardware architectures
that do not support mid-circuit measurements.Comment: 24 pages, 19 figure
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