Space-efficient simulation of quantum computers

Abstract

Traditional algorithms for simulating quantum computers on classical ones require an exponentially large amount of memory, and so typically cannot simulate general quantum circuits with more than about 30 or so qubits on a typical PC-scale platform with only a few gigabytes of main memory. However, more memory-efficient simulations are possible, requiring only polynomial or even linear space in the size of the quantum circuit being simulated. In this paper, we describe one such technique, which was recently implemented at FSU in the form of a C++ program called SEQCSIM, which we releasing publicly. We also discuss the potential benefits of this simulation in quantum computing research and education, and outline some possible directions for further progress.

A space-efficient quantum computer simulator suitable for high-speed FPGA implementation

“…1 qopseq.txt format version 1 2 operations: 30 3 operation #0: apply unary operator H to bits a [3] 4 operation #1: apply binary operator cPiOver2 to bits a [3], a [2] 5 operation #2: apply binary operator cPiOver4 to bits a [3], a [1] 6 operation #3: apply binary operator cPiOver8 to bits a [3], a[0]…”

“…The basic concept is simply to recalculate data When the complexity theory of quantum computing was being developed in the early 1990s, it was quickly realized [2] that the same idea, back now in the discrete realm, could be applied to the simulation of quantum computers as well, leading to the important complexity-theoretic relation that BQP ⊆ PSPACE, where BQP is the set of problems solvable by probabilistic quantum algorithms with a polynomial number of operations (as a function of problem size), and PSPACE is the set of problems solvable by classical computers using a polynomial amount of memory. More generally, we can show [3] that a quantum algorithm with s qubits and t operations can be simulated using space O(s + t).…”

The case for biological quantum computer elements

“…To see a detailed graphical illustration of the functioning of this algorithm on a particularly simple example circuit, please refer to our previous paper [3] .…”

“…More generally, we can show [3] that a quantum algorithm with s qubits and t operations can be simulated using space O(s + t).…”

A Fast Quantum Computer Simulator Based on Register Reordering

“…However, the number of quantum bits and quantum gates that can be simulated are still limited. In [3], [4], a space efficient quantum computer simulator is proposed. This is based on the fact that BQP is included in PSPACE, where BQP is the class of decision problems that can be solved by quantum Turing machines in polynomial time with bounded error, and PSPACE is the class of decision problems that can be solved by classical Turing machines in polynomial space.…”