11 research outputs found
Optimal Quantum Circuits for Nearest-Neighbor Architectures
We show that the depth of quantum circuits in the realistic architecture
where a classical controller determines which local interactions to apply on
the kD grid Z^k where k >= 2 is the same (up to a constant factor) as in the
standard model where arbitrary interactions are allowed. This allows
minimum-depth circuits (up to a constant factor) for the nearest-neighbor
architecture to be obtained from minimum-depth circuits in the standard
abstract model. Our work therefore justifies the standard assumption that
interactions can be performed between arbitrary pairs of qubits. In particular,
our results imply that Shor's algorithm, controlled operations and fanouts can
be implemented in constant depth, polynomial size and polynomial width in this
architecture.
We also present optimal non-adaptive quantum circuits for controlled
operations and fanouts on a kD grid. These circuits have depth Theta(n^(1 /
k)), size Theta(n) and width Theta(n). Our lower bound also applies to a more
general class of operations.Comment: 24 pages, 6 figures. v1 introduces all the results. v2 and v3 make
minor improvements to the presentation and add additional reference
Limits on Fundamental Limits to Computation
An indispensable part of our lives, computing has also become essential to
industries and governments. Steady improvements in computer hardware have been
supported by periodic doubling of transistor densities in integrated circuits
over the last fifty years. Such Moore scaling now requires increasingly heroic
efforts, stimulating research in alternative hardware and stirring controversy.
To help evaluate emerging technologies and enrich our understanding of
integrated-circuit scaling, we review fundamental limits to computation: in
manufacturing, energy, physical space, design and verification effort, and
algorithms. To outline what is achievable in principle and in practice, we
recall how some limits were circumvented, compare loose and tight limits. We
also point out that engineering difficulties encountered by emerging
technologies may indicate yet-unknown limits.Comment: 15 pages, 4 figures, 1 tabl
Exploiting Quantum Teleportation in Quantum Circuit Mapping
Quantum computers are constantly growing in their number of qubits, but
continue to suffer from restrictions such as the limited pairs of qubits that
may interact with each other. Thus far, this problem is addressed by mapping
and moving qubits to suitable positions for the interaction (known as quantum
circuit mapping). However, this movement requires additional gates to be
incorporated into the circuit, whose number should be kept as small as possible
since each gate increases the likelihood of errors and decoherence.
State-of-the-art mapping methods utilize swapping and bridging to move the
qubits along the static paths of the coupling map---solving this problem
without exploiting all means the quantum domain has to offer. In this paper, we
propose to additionally exploit quantum teleportation as a possible
complementary method. Quantum teleportation conceptually allows to move the
state of a qubit over arbitrary long distances with constant
overhead---providing the potential of determining cheaper mappings. The
potential is demonstrated by a case study on the IBM Q Tokyo architecture which
already shows promising improvements. With the emergence of larger quantum
computing architectures, quantum teleportation will become more effective in
generating cheaper mappings.Comment: To appear in ASP-DAC 202
Space-time optimized table lookup
We describe a space-time optimized circuit for the table lookup subroutine
from lattice-surgery surface code primitives respecting 2D grid connectivity.
Table lookup circuits are ubiquitous in quantum computing, allowing the
presented circuit to be used for applications ranging from cryptography to
quantum chemistry. Surface code is the leading approach to scalable
fault-tolerant quantum computing pursued by industry and academia. We abstract
away surface code implementation details by using a minimal set of operations
supported by the surface code via lattice-surgery. Our exposition is accessible
to a reader not familiar with surface codes and fault-tolerant quantum
computing.Comment: 27 page
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