Gate-level simulation of quantum circuits

Abstract

While thousands of experimental physicists and chemists are currently trying to build scalable quantum computers, it appears that simulation of quantum computation will be at least as critical as circuit simulation in classical VLSI design. However, since the work of Richard Feynman in the early 1980s little progress was made in practical quantum simulation. Most researchers focused on polynomial-time simulation of restricted types of quantum circuits that fall short of the full power of quantum computation [7].Simulating quantum computing devices and useful quantum algorithms on classical hardware now requires excessive computational resources, making many important simulation tasks infeasible. In this work we propose a new technique for gate-level simulation of quantum circuits which greatly reduces the difficulty and cost of such simulations. The proposed technique is implemented in a simulation tool called the Quantum Information Decision Diagram (QuIDD) and evaluated by simulating Grover's quantum search algorithm [8]. The back-end of our package, QuIDD Pro, is based on Binary Decision Diagrams, well-known for their ability to efficiently represent many seemingly intractable combinatorial structures. This reliance on a well-established area of research allows us to take advantage of existing software for BDD manipulation and achieve unparalleled empirical results for quantum simulation.

Binary superposed quantum decision diagrams

“…This is different from other quantum decision diagrams such as QuIDDs [14] and QMDDs [7] which focus on providing efficient representations of quantum operators and states rather than synthesizing quantum arrays for initialization. BSQDDs also differ from QDDs [1] which are used for synthesizing operators rather than states.…”

“…Quantum decision diagrams called quantum information decision diagrams (QuIDDs) were first created by Viamontes et al [13,14] for representing quantum operators and states. Miller and Thornton [7] developed improved decision diagrams called quantum multivalued decision diagrams (QMDDs) for representing binary and multivalued quantum operators.…”

Debugging reversible circuits

“…[6][7][8][11][12][13][14][15]). Furthermore, simulation [16,17], optimization [18,19], testing [20,21,9], and verification [22][23][24] have been investigated. However, to the best of our knowledge the problem of debugging has not been considered yet.…”

Test Generation and Fault Localization for Quantum Circuits

“…It is assumed that the reader is familiar with classical testing fundamentals, basic quantum gates, unitary matrix calculus of quantum mechanics and simulation. Information about test generation and fault localization can be found in [7] and quantum textbooks like [10], as well as papers [14,15] are recommended.…”

“…They will solve some problems never possible with standard computers and they will be super-fast and super-small in size for standard applications. Quantum logic gate [1,3,4,5,6,8,9,10,11,14,15,30] is a device which performs an operation described by a unitary matrix on selected qubits (quantum bits, [10]). Binary quantum gates process qubits which can have either a |0> or |1> or both |0> and |1> at the same time to varying extents and hence exhibit a superposition state |0>+ |1> where | | 2 + | | 2 = 1, and are complex numbers such that measurement probability of |0> is | | 2 and measurement probability of |1> is | | 2 .…”