480 research outputs found
Synthesis and Optimization of Reversible Circuits - A Survey
Reversible logic circuits have been historically motivated by theoretical
research in low-power electronics as well as practical improvement of
bit-manipulation transforms in cryptography and computer graphics. Recently,
reversible circuits have attracted interest as components of quantum
algorithms, as well as in photonic and nano-computing technologies where some
switching devices offer no signal gain. Research in generating reversible logic
distinguishes between circuit synthesis, post-synthesis optimization, and
technology mapping. In this survey, we review algorithmic paradigms ---
search-based, cycle-based, transformation-based, and BDD-based --- as well as
specific algorithms for reversible synthesis, both exact and heuristic. We
conclude the survey by outlining key open challenges in synthesis of reversible
and quantum logic, as well as most common misconceptions.Comment: 34 pages, 15 figures, 2 table
Qubit Mapping Toward Quantum Advantage
Qubit Mapping is a pivotal stage in quantum compilation flow. Its goal is to
convert logical circuits into physical circuits so that a quantum algorithm can
be executed on real-world non-fully connected quantum devices. Qubit Mapping
techniques nowadays still lack the key to quantum advantage, scalability.
Several studies have proved that at least thousands of logical qubits are
required to achieve quantum computational advantage. However, to our best
knowledge, there is no previous research with the ability to solve the qubit
mapping problem with the necessary number of qubits for quantum advantage in a
reasonable time. In this work, we provide the first qubit mapping framework
with the scalability to achieve quantum advantage while accomplishing a fairly
good performance. The framework also boasts its flexibility for quantum
circuits of different characteristics. Experimental results show that the
proposed mapping method outperforms the state-of-the-art methods on quantum
circuit benchmarks by improving over 5% of the cost complexity in one-tenth of
the program running time. Moreover, we demonstrate the scalability of our
method by accomplishing mapping of an 11,969-qubit Quantum Fourier Transform
within five hours
Reducing the CNOT count for Clifford+T circuits on NISQ architectures
While mapping a quantum circuit to the physical layer one has to consider the
numerous constraints imposed by the underlying hardware architecture.
Connectivity of the physical qubits is one such constraint that restricts
two-qubit operations such as CNOT to "connected" qubits. SWAP gates can be used
to place the logical qubits on admissible physical qubits, but they entail a
significant increase in CNOT-count, considering the fact that each SWAP gate
can be implemented by 3 CNOT gates.
In this paper we consider the problem of reducing the CNOT-count in
Clifford+T circuits on connectivity constrained architectures such as noisy
intermediate-scale quantum (NISQ) (Preskill, 2018) computing devices. We
"slice" the circuit at the position of Hadamard gates and "build" the
intermediate portions. We investigated two kinds of partitioning - (i) a simple
method of partitioning the gates of the input circuit based on the locality of
H gates and (ii) a second method of partitioning the phase polynomial of the
input circuit. The intermediate {CNOT,T} sub-circuits are synthesized using
Steiner trees, significantly improving on the methods introduced by Nash,
Gheorghiu, Mosca[2020] and Kissinger, de Griend[2019].
We compared the performance of our algorithms while mapping different
benchmark circuits as well as random circuits to some popular architectures
such as 9-qubit square grid, 16-qubit square grid, Rigetti 16-qubit Aspen,
16-qubit IBM QX5 and 20-qubit IBM Tokyo. We found that for both the benchmark
and random circuits our first algorithm that uses the simple slicing technique
dramatically reduces the CNOT-count compared to naively using SWAP gates. Our
second slice-and-build algorithm also performs very well for benchmark
circuits.Comment: 41 pages, 2 figures, 2 tables. Added appendix with example
Mathematical formulation of quantum circuit design problems in networks of quantum computers
In quantum circuit design, the question arises how to distribute qubits, used in algorithms, over the various quantum computers, and how to order them within a quantum computer. In order to evaluate these problems, we define the global and local reordering problems for distributed quantum computing. We formalise the mathematical problems and model them as integer linear programming problems, to minimise the number of SWAP gates or the number of interactions between different quantum computers. For global reordering, we analyse the problem for various geometries of networks: completely connected networks, general networks, linear arrays and grid-structured networks. For local reordering, in networks of quantum computers, we also define the mathematical optimisation problem
Computational Capabilities and Compiler Development for Neutral Atom Quantum Processors: Connecting Tool Developers and Hardware Experts
Neutral Atom Quantum Computing (NAQC) emerges as a promising hardware
platform primarily due to its long coherence times and scalability.
Additionally, NAQC offers computational advantages encompassing potential
long-range connectivity, native multi-qubit gate support, and the ability to
physically rearrange qubits with high fidelity. However, for the successful
operation of a NAQC processor, one additionally requires new software tools to
translate high-level algorithmic descriptions into a hardware executable
representation, taking maximal advantage of the hardware capabilities.
Realizing new software tools requires a close connection between tool
developers and hardware experts to ensure that the corresponding software tools
obey the corresponding physical constraints. This work aims to provide a basis
to establish this connection by investigating the broad spectrum of
capabilities intrinsic to the NAQC platform and its implications on the
compilation process. To this end, we first review the physical background of
NAQC and derive how it affects the overall compilation process by formulating
suitable constraints and figures of merit. We then provide a summary of the
compilation process and discuss currently available software tools in this
overview. Finally, we present selected case studies and employ the discussed
figures of merit to evaluate the different capabilities of NAQC and compare
them between two hardware setups.Comment: 32 pages, 13 figures, 2 table
Circuit Transformations for Quantum Architectures
Quantum computer architectures impose restrictions on qubit interactions. We propose efficient circuit transformations that modify a given quantum circuit to fit an architecture, allowing for any initial and final mapping of circuit qubits to architecture qubits. To achieve this, we first consider the qubit movement subproblem and use the ROUTING VIA MATCHINGS framework to prove tighter bounds on parallel routing. In practice, we only need to perform partial permutations, so we generalize ROUTING VIA MATCHINGS to that setting. We give new routing procedures for common architecture graphs and for the generalized hierarchical product of graphs, which produces subgraphs of the Cartesian product. Secondly, for serial routing, we consider the TOKEN SWAPPING framework and extend a 4-approximation algorithm for general graphs to support partial permutations. We apply these routing procedures to give several circuit transformations, using various heuristic qubit placement subroutines. We implement these transformations in software and compare their performance for large quantum circuits on grid and modular architectures, identifying strategies that work well in practice
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