1,030 research outputs found
QuBEC: Boosting Equivalence Checking for Quantum Circuits with QEC Embedding
Quantum computing has proven to be capable of accelerating many algorithms by
performing tasks that classical computers cannot. Currently, Noisy Intermediate
Scale Quantum (NISQ) machines struggle from scalability and noise issues to
render a commercial quantum computer. However, the physical and software
improvements of a quantum computer can efficiently control quantum gate noise.
As the complexity of quantum algorithms and implementation increases, software
control of quantum circuits may lead to a more intricate design. Consequently,
the verification of quantum circuits becomes crucial in ensuring the
correctness of the compilation, along with other processes, including quantum
error correction and assertions, that can increase the fidelity of quantum
circuits. In this paper, we propose a Decision Diagram-based quantum
equivalence checking approach, QuBEC, that requires less latency compared to
existing techniques, while accounting for circuits with quantum error
correction redundancy. Our proposed methodology reduces verification time on
certain benchmark circuits by up to , while the number of
Decision Diagram nodes required is reduced by up to , compared
to state-of-the-art strategies. The proposed QuBEC framework can contribute to
the advancement of quantum computing by enabling faster and more efficient
verification of quantum circuits, paving the way for the development of larger
and more complex quantum algorithms
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
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
Approximation of Quantum States Using Decision Diagrams
The computational power of quantum computers poses major challenges to new
design tools since representing pure quantum states typically requires
exponentially large memory. As shown previously, decision diagrams can reduce
these memory requirements by exploiting redundancies. In this work, we
demonstrate further reductions by allowing for small inaccuracies in the
quantum state representation. Such inaccuracies are legitimate since quantum
computers themselves experience gate and measurement errors and since quantum
algorithms are somewhat resistant to errors (even without error correction). We
develop four dedicated schemes that exploit these observations and effectively
approximate quantum states represented by decision diagrams. We empirically
show that the proposed schemes reduce the size of decision diagrams by up to
several orders of magnitude while controlling the fidelity of approximate
quantum state representations
LIMDD A Decision Diagram for Simulation of Quantum Computing Including Stabilizer States
Efficient methods for the representation and simulation of quantum states and
quantum operations are crucial for the optimization of quantum circuits.
Decision diagrams (DDs), a well-studied data structure originally used to
represent Boolean functions, have proven capable of capturing relevant aspects
of quantum systems, but their limits are not well understood. In this work, we
investigate and bridge the gap between existing DD-based structures and the
stabilizer formalism, an important tool for simulating quantum circuits in the
tractable regime. We first show that although DDs were suggested to succinctly
represent important quantum states, they actually require exponential space for
certain stabilizer states. To remedy this, we introduce a more powerful
decision diagram variant, called Local Invertible Map-DD (LIMDD). We prove that
the set of quantum states represented by poly-sized LIMDDs strictly contains
the union of stabilizer states and other decision diagram variants. Finally,
there exist circuits which LIMDDs can efficiently simulate, but which cannot be
efficiently simulated by two state-of-the-art simulation paradigms: the
Clifford + T simulator and Matrix-Product States. By uniting two successful
approaches, LIMDDs thus pave the way for fundamentally more powerful solutions
for simulation and analysis of quantum computing
Just Like the Real Thing: Fast Weak Simulation of Quantum Computation
Quantum computers promise significant speedups in solving problems
intractable for conventional computers but, despite recent progress, remain
limited in scaling and availability. Therefore, quantum software and hardware
development heavily rely on simulation that runs on conventional computers.
Most such approaches perform strong simulation in that they explicitly compute
amplitudes of quantum states. However, such information is not directly
observable from a physical quantum computer because quantum measurements
produce random samples from probability distributions defined by those
amplitudes. In this work, we focus on weak simulation that aims to produce
outputs which are statistically indistinguishable from those of error-free
quantum computers. We develop algorithms for weak simulation based on quantum
state representation in terms of decision diagrams. We compare them to using
state-vector arrays and binary search on prefix sums to perform sampling.
Empirical validation shows, for the first time, that this enables mimicking of
physical quantum computers of significant scale.Comment: 6 pages, 4 figure
Reversible Computation: Extending Horizons of Computing
This open access State-of-the-Art Survey presents the main recent scientific outcomes in the area of reversible computation, focusing on those that have emerged during COST Action IC1405 "Reversible Computation - Extending Horizons of Computing", a European research network that operated from May 2015 to April 2019. Reversible computation is a new paradigm that extends the traditional forwards-only mode of computation with the ability to execute in reverse, so that computation can run backwards as easily and naturally as forwards. It aims to deliver novel computing devices and software, and to enhance existing systems by equipping them with reversibility. There are many potential applications of reversible computation, including languages and software tools for reliable and recovery-oriented distributed systems and revolutionary reversible logic gates and circuits, but they can only be realized and have lasting effect if conceptual and firm theoretical foundations are established first
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