68,218 research outputs found
Low-cost error mitigation by symmetry verification
We investigate the performance of error mitigation via measurement of
conserved symmetries on near-term devices. We present two protocols to measure
conserved symmetries during the bulk of an experiment, and develop a zero-cost
post-processing protocol which is equivalent to a variant of the quantum
subspace expansion. We develop methods for inserting global and local symetries
into quantum algorithms, and for adjusting natural symmetries of the problem to
boost their mitigation against different error channels. We demonstrate these
techniques on two- and four-qubit simulations of the hydrogen molecule (using a
classical density-matrix simulator), finding up to an order of magnitude
reduction of the error in obtaining the ground state dissociation curve.Comment: Published versio
Quantum walk speedup of backtracking algorithms
We describe a general method to obtain quantum speedups of classical
algorithms which are based on the technique of backtracking, a standard
approach for solving constraint satisfaction problems (CSPs). Backtracking
algorithms explore a tree whose vertices are partial solutions to a CSP in an
attempt to find a complete solution. Assume there is a classical backtracking
algorithm which finds a solution to a CSP on n variables, or outputs that none
exists, and whose corresponding tree contains T vertices, each vertex
corresponding to a test of a partial solution. Then we show that there is a
bounded-error quantum algorithm which completes the same task using O(sqrt(T)
n^(3/2) log n) tests. In particular, this quantum algorithm can be used to
speed up the DPLL algorithm, which is the basis of many of the most efficient
SAT solvers used in practice. The quantum algorithm is based on the use of a
quantum walk algorithm of Belovs to search in the backtracking tree. We also
discuss how, for certain distributions on the inputs, the algorithm can lead to
an exponential reduction in expected runtime.Comment: 23 pages; v2: minor changes to presentatio
The Quantum Decoding Problem
One of the founding results of lattice based cryptography is a quantum
reduction from the Short Integer Solution problem to the Learning with Errors
problem introduced by Regev. It has recently been pointed out by Chen, Liu and
Zhandry that this reduction can be made more powerful by replacing the learning
with errors problem with a quantum equivalent, where the errors are given in
quantum superposition. In the context of codes, this can be adapted to a
reduction from finding short codewords to a quantum decoding problem for random
linear codes.
We therefore consider in this paper the quantum decoding problem, where we
are given a superposition of noisy versions of a codeword and we want to
recover the corresponding codeword. When we measure the superposition, we get
back the usual classical decoding problem for which the best known algorithms
are in the constant rate and error-rate regime exponential in the codelength.
However, we will show here that when the noise rate is small enough, then the
quantum decoding problem can be solved in quantum polynomial time. Moreover, we
also show that the problem can in principle be solved quantumly (albeit not
efficiently) for noise rates for which the associated classical decoding
problem cannot be solved at all for information theoretic reasons.
We then revisit Regev's reduction in the context of codes. We show that using
our algorithms for the quantum decoding problem in Regev's reduction matches
the best known quantum algorithms for the short codeword problem. This shows in
some sense the tightness of Regev's reduction when considering the quantum
decoding problem and also paves the way for new quantum algorithms for the
short codeword problem
System Design for a Long-Line Quantum Repeater
We present a new control algorithm and system design for a network of quantum
repeaters, and outline the end-to-end protocol architecture. Such a network
will create long-distance quantum states, supporting quantum key distribution
as well as distributed quantum computation. Quantum repeaters improve the
reduction of quantum-communication throughput with distance from exponential to
polynomial. Because a quantum state cannot be copied, a quantum repeater is not
a signal amplifier, but rather executes algorithms for quantum teleportation in
conjunction with a specialized type of quantum error correction called
purification to raise the fidelity of the quantum states. We introduce our
banded purification scheme, which is especially effective when the fidelity of
coupled qubits is low, improving the prospects for experimental realization of
such systems. The resulting throughput is calculated via detailed simulations
of a long line composed of shorter hops. Our algorithmic improvements increase
throughput by a factor of up to fifty compared to earlier approaches, for a
broad range of physical characteristics.Comment: 12 pages, 13 figures. v2 includes one new graph, modest corrections
to some others, and significantly improved presentation. to appear in
IEEE/ACM Transactions on Networkin
Optimal and Efficient Decoding of Concatenated Quantum Block Codes
We consider the problem of optimally decoding a quantum error correction code
-- that is to find the optimal recovery procedure given the outcomes of partial
"check" measurements on the system. In general, this problem is NP-hard.
However, we demonstrate that for concatenated block codes, the optimal decoding
can be efficiently computed using a message passing algorithm. We compare the
performance of the message passing algorithm to that of the widespread
blockwise hard decoding technique. Our Monte Carlo results using the 5 qubit
and Steane's code on a depolarizing channel demonstrate significant advantages
of the message passing algorithms in two respects. 1) Optimal decoding
increases by as much as 94% the error threshold below which the error
correction procedure can be used to reliably send information over a noisy
channel. 2) For noise levels below these thresholds, the probability of error
after optimal decoding is suppressed at a significantly higher rate, leading to
a substantial reduction of the error correction overhead.Comment: Published versio
Magic-State Functional Units: Mapping and Scheduling Multi-Level Distillation Circuits for Fault-Tolerant Quantum Architectures
Quantum computers have recently made great strides and are on a long-term
path towards useful fault-tolerant computation. A dominant overhead in
fault-tolerant quantum computation is the production of high-fidelity encoded
qubits, called magic states, which enable reliable error-corrected computation.
We present the first detailed designs of hardware functional units that
implement space-time optimized magic-state factories for surface code
error-corrected machines. Interactions among distant qubits require surface
code braids (physical pathways on chip) which must be routed. Magic-state
factories are circuits comprised of a complex set of braids that is more
difficult to route than quantum circuits considered in previous work [1]. This
paper explores the impact of scheduling techniques, such as gate reordering and
qubit renaming, and we propose two novel mapping techniques: braid repulsion
and dipole moment braid rotation. We combine these techniques with graph
partitioning and community detection algorithms, and further introduce a
stitching algorithm for mapping subgraphs onto a physical machine. Our results
show a factor of 5.64 reduction in space-time volume compared to the best-known
previous designs for magic-state factories.Comment: 13 pages, 10 figure
- …