2,456 research outputs found
Polynomial-time T-depth Optimization of Clifford+T circuits via Matroid Partitioning
Most work in quantum circuit optimization has been performed in isolation
from the results of quantum fault-tolerance. Here we present a polynomial-time
algorithm for optimizing quantum circuits that takes the actual implementation
of fault-tolerant logical gates into consideration. Our algorithm
re-synthesizes quantum circuits composed of Clifford group and T gates, the
latter being typically the most costly gate in fault-tolerant models, e.g.,
those based on the Steane or surface codes, with the purpose of minimizing both
T-count and T-depth. A major feature of the algorithm is the ability to
re-synthesize circuits with additional ancillae to reduce T-depth at
effectively no cost. The tested benchmarks show up to 65.7% reduction in
T-count and up to 87.6% reduction in T-depth without ancillae, or 99.7%
reduction in T-depth using ancillae.Comment: Version 2 contains substantial improvements and extensions to the
previous version. We describe a new, more robust algorithm and achieve
significantly improved experimental result
Lower bounds on the non-Clifford resources for quantum computations
We establish lower-bounds on the number of resource states, also known as
magic states, needed to perform various quantum computing tasks, treating
stabilizer operations as free. Our bounds apply to adaptive computations using
measurements and an arbitrary number of stabilizer ancillas. We consider (1)
resource state conversion, (2) single-qubit unitary synthesis, and (3)
computational tasks.
To prove our resource conversion bounds we introduce two new monotones, the
stabilizer nullity and the dyadic monotone, and make use of the already-known
stabilizer extent. We consider conversions that borrow resource states, known
as catalyst states, and return them at the end of the algorithm. We show that
catalysis is necessary for many conversions and introduce new catalytic
conversions, some of which are close to optimal.
By finding a canonical form for post-selected stabilizer computations, we
show that approximating a single-qubit unitary to within diamond-norm precision
requires at least
-states on average. This is the first lower bound that applies to synthesis
protocols using fall-back, mixing techniques, and where the number of ancillas
used can depend on .
Up to multiplicative factors, we optimally lower bound the number of or
states needed to implement the ubiquitous modular adder and
multiply-controlled- operations. When the probability of Pauli measurement
outcomes is 1/2, some of our bounds become tight to within a small additive
constant.Comment: 62 page
Quadratic Form Expansions for Unitaries
We introduce techniques to analyze unitary operations in terms of quadratic
form expansions, a form similar to a sum over paths in the computational basis
when the phase contributed by each path is described by a quadratic form over
. We show how to relate such a form to an entangled resource akin to
that of the one-way measurement model of quantum computing. Using this, we
describe various conditions under which it is possible to efficiently implement
a unitary operation U, either when provided a quadratic form expansion for U as
input, or by finding a quadratic form expansion for U from other input data.Comment: 20 pages, 3 figures; (extended version of) accepted submission to TQC
200
Programming Quantum Computers Using Design Automation
Recent developments in quantum hardware indicate that systems featuring more
than 50 physical qubits are within reach. At this scale, classical simulation
will no longer be feasible and there is a possibility that such quantum devices
may outperform even classical supercomputers at certain tasks. With the rapid
growth of qubit numbers and coherence times comes the increasingly difficult
challenge of quantum program compilation. This entails the translation of a
high-level description of a quantum algorithm to hardware-specific low-level
operations which can be carried out by the quantum device. Some parts of the
calculation may still be performed manually due to the lack of efficient
methods. This, in turn, may lead to a design gap, which will prevent the
programming of a quantum computer. In this paper, we discuss the challenges in
fully-automatic quantum compilation. We motivate directions for future research
to tackle these challenges. Yet, with the algorithms and approaches that exist
today, we demonstrate how to automatically perform the quantum programming flow
from algorithm to a physical quantum computer for a simple algorithmic
benchmark, namely the hidden shift problem. We present and use two tool flows
which invoke RevKit. One which is based on ProjectQ and which targets the IBM
Quantum Experience or a local simulator, and one which is based on Microsoft's
quantum programming language Q.Comment: 10 pages, 10 figures. To appear in: Proceedings of Design, Automation
and Test in Europe (DATE 2018
Fast and efficient exact synthesis of single qubit unitaries generated by Clifford and T gates
In this paper, we show the equivalence of the set of unitaries computable by
the circuits over the Clifford and T library and the set of unitaries over the
ring , in the single-qubit case. We report an
efficient synthesis algorithm, with an exact optimality guarantee on the number
of Hadamard and T gates used. We conjecture that the equivalence of the sets of
unitaries implementable by circuits over the Clifford and T library and
unitaries over the ring holds in the
-qubit case.Comment: 23 pages, 3 figures, added the proof of T-optimality of the circuits
synthesized by Algorithm
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