23 research outputs found
Mapping constrained optimization problems to quantum annealing with application to fault diagnosis
Current quantum annealing (QA) hardware suffers from practical limitations
such as finite temperature, sparse connectivity, small qubit numbers, and
control error. We propose new algorithms for mapping boolean constraint
satisfaction problems (CSPs) onto QA hardware mitigating these limitations. In
particular we develop a new embedding algorithm for mapping a CSP onto a
hardware Ising model with a fixed sparse set of interactions, and propose two
new decomposition algorithms for solving problems too large to map directly
into hardware.
The mapping technique is locally-structured, as hardware compatible Ising
models are generated for each problem constraint, and variables appearing in
different constraints are chained together using ferromagnetic couplings. In
contrast, global embedding techniques generate a hardware independent Ising
model for all the constraints, and then use a minor-embedding algorithm to
generate a hardware compatible Ising model. We give an example of a class of
CSPs for which the scaling performance of D-Wave's QA hardware using the local
mapping technique is significantly better than global embedding.
We validate the approach by applying D-Wave's hardware to circuit-based
fault-diagnosis. For circuits that embed directly, we find that the hardware is
typically able to find all solutions from a min-fault diagnosis set of size N
using 1000N samples, using an annealing rate that is 25 times faster than a
leading SAT-based sampling method. Further, we apply decomposition algorithms
to find min-cardinality faults for circuits that are up to 5 times larger than
can be solved directly on current hardware.Comment: 22 pages, 4 figure
Revisiting old combinatorial beasts in the quantum age: quantum annealing versus maximal matching
This paper experimentally investigates the behavior of analog quantum computers such as commercialized by D-Wave when confronted to instances of the maximum cardinality matching problem specifically designed to be hard to solve by means of simulated annealing. We benchmark a D-Wave "Washington" (2X) with 1098 operational qubits on various sizes of such instances and observe that for all but the most trivially small of these it fails to obtain an optimal solution. Thus, our results suggests that quantum annealing, at least as implemented in a D-Wave device, falls in the same pitfalls as simulated annealing and therefore suggest that there exist polynomial-time problems that such a machine cannot solve efficiently to optimality
Effective Prime Factorization via Quantum Annealing by Modular Locally-structured Embedding
This paper investigates novel techniques to solve prime factorization by
quantum annealing (QA). Our contribution is twofold. First, we present a novel
and very compact modular encoding of a binary multiplier circuit into the
Pegasus architecture of current D-Wave QA devices. The key contribution is a
compact encoding of a controlled full-adder into an 8-qubit module in the
Pegasus topology, which we synthesized offline by means of Optimization Modulo
Theories. This allows us to encode up to a 21*12-bit multiplier (and a 22*8-bit
one) into the Pegasus 5760-qubit topology of current annealers. To the best of
our knowledge, these are the largest factorization problems ever encoded into a
quantum annealer. Second, we have investigated the problem of actually solving
encoded PF problems by running an extensive experimental evaluation on a D-Wave
Advantage 4.1 quantum annealer. In order to help the annealer in reaching the
global minimum, in the experiments we introduced different approaches to
initialize the multiplier qubits and adopted several performance enhancement
techniques. Overall, exploiting all the encoding and solving techniques
described in this paper, 8, 219, 999 = 32, 749 * 251 was the highest prime
product we were able to factorize within the limits of our QPU resources. To
the best of our knowledge, this is the largest number which was ever factorized
by means of a quantum annealer, and, more generally, by a quantum device