24 research outputs found
Equivalence Checking of Sequential Quantum Circuits
We define a formal framework for equivalence checking of sequential quantum
circuits. The model we adopted is a quantum state machine, which is a natural
quantum generalisation of Mealy machines. A major difficulty in checking
quantum circuits (but not present in checking classical circuits) is that the
state spaces of quantum circuits are continuums. This difficulty is resolved by
our main theorem showing that equivalence checking of two quantum Mealy
machines can be done with input sequences that are taken from some chosen basis
(which are finite) and have a length quadratic in the dimensions of the state
Hilbert spaces of the machines. Based on this theoretical result, we develop an
(and to the best of our knowledge, the first) algorithm for checking
equivalence of sequential quantum circuits. A case study and experiments are
presented
Handling Non-Unitaries in Quantum Circuit Equivalence Checking
Quantum computers are reaching a level where interactions between classical
and quantum computations can happen in real-time. This marks the advent of a
new, broader class of quantum circuits: dynamic quantum circuits. They offer a
broader range of available computing primitives that lead to new challenges for
design tasks such as simulation, compilation, and verification. Due to the
non-unitary nature of dynamic circuit primitives, most existing techniques and
tools for these tasks are no longer applicable in an out-of-the-box fashion. In
this work, we discuss the resulting consequences for quantum circuit
verification, specifically equivalence checking, and propose two different
schemes that eventually allow to treat the involved circuits as if they did not
contain non-unitaries at all. As a result, we demonstrate methodically, as well
as, experimentally that existing techniques for verifying the equivalence of
quantum circuits can be kept applicable for this broader class of circuits.Comment: 7 pages, 4 figures, old title: "Towards Verification of Dynamic
Quantum Circuits", revised manuscript, added experimental result
Fast equivalence checking of quantum circuits of Clifford gates
Checking whether two quantum circuits are equivalent is important for the
design and optimization of quantum-computer applications with real-world
devices. We consider quantum circuits consisting of Clifford gates, a
practically-relevant subset of all quantum operations which is large enough to
exhibit quantum features such as entanglement and forms the basis of, for
example, quantum-error correction and many quantum-network applications. We
present a deterministic algorithm that is based on a folklore mathematical
result and demonstrate that it is capable of outperforming previously
considered state-of-the-art method. In particular, given two Clifford circuits
as sequences of single- and two-qubit Clifford gates, the algorithm checks
their equivalence in time in the number of qubits and number
of elementary Clifford gates . Using the performant Stim simulator as
backend, our implementation checks equivalence of quantum circuits with 1000
qubits (and a circuit depth of 10.000 gates) in 22 seconds and circuits
with 100.000 qubits (depth 10) in 15 minutes, outperforming the existing
SAT-based and path-integral based approaches by orders of magnitude. This
approach shows that the correctness of application-relevant subsets of quantum
operations can be verified up to large circuits in practice
Verifying Results of the IBM Qiskit Quantum Circuit Compilation Flow
Realizing a conceptual quantum algorithm on an actual physical device
necessitates the algorithm's quantum circuit description to undergo certain
transformations in order to adhere to all constraints imposed by the hardware.
In this regard, the individual high-level circuit components are first
synthesized to the supported low-level gate-set of the quantum computer, before
being mapped to the target's architecture---utilizing several optimizations in
order to improve the compilation result. Specialized tools for this complex
task exist, e.g., IBM's Qiskit, Google's Cirq, Microsoft's QDK, or Rigetti's
Forest. However, to date, the circuits resulting from these tools are hardly
verified, which is mainly due to the immense complexity of checking if two
quantum circuits indeed realize the same functionality. In this paper, we
propose an efficient scheme for quantum circuit equivalence
checking---specialized for verifying results of the IBM Qiskit quantum circuit
compilation flow. To this end, we combine characteristics unique to quantum
computing, e.g., its inherent reversibility, and certain knowledge about the
compilation flow into a dedicated equivalence checking strategy. Experimental
evaluations confirm that the proposed scheme allows to verify even large
circuit instances with tens of thousands of operations within seconds or even
less, whereas state-of-the-art techniques frequently time-out or require
substantially more runtime. A corresponding open source implementation of the
proposed method is publicly available at https://github.com/iic-jku/qcec.Comment: 10 pages, to be published at International Conference on Quantum
Computing and Engineering (QCE20
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