Quantum algorithms and circuits for scientific computing

Chen

et al. 2021

Sci Rep

Classical simulation of quantum computation is vital for verifying quantum devices and assessing quantum algorithms. We present a new quantum circuit simulator developed on the Sunway TaihuLight supercomputer. Compared with other simulators, the present one is distinguished in two aspects. First, our simulator is more versatile. The simulator consists of three mutually independent parts to compute the full, partial and single amplitudes of a quantum state with different methods. It has the function of emulating the effect of noise and support more kinds of quantum operations. Second, our simulator is of high efficiency. The simulator is designed in a two-level parallel structure to be implemented efficiently on the distributed many-core Sunway TaihuLight supercomputer. Random quantum circuits can be simulated with 40, 75 and 200 qubits on the full, partial and single amplitude, respectively. As illustrative applications of the simulator, we present a quantum fast Poisson solver and an algorithm for quantum arithmetic of evaluating transcendental functions. Our simulator is expected to have broader applications in developing quantum algorithms in various fields.

Section: Quantum Arithmetic Of Transcendental Functionsmentioning

confidence: 99%

A quantum circuit simulator and its applications on Sunway TaihuLight supercomputer

Chen

et al. 2021

Sci Rep

“…It is not clear if and how these classical algorithm can be realized in a quantum circuit of same asymptotic complexity. The current research on implementing transcendental functions, like trigonometric functions, on quantum computers is sparse [41][42][43][44]. Wang et al recently proposed an algorithm that can realize our desired classical computation using OpB 3 q operations and OpB 2 q qubits [44].…”

Section: Circuit Complexitymentioning

confidence: 99%

Quantum message-passing algorithm for optimal and efficient decoding

Piveteau¹,

Renes²

2021

Preprint

Recently, Renes proposed a quantum algorithm called belief propagation with quantum messages (BPQM) for decoding classical data encoded using a binary linear code with tree Tanner graph that is transmitted over a pure-state CQ channel [1]. The algorithm presents a genuine quantum counterpart to decoding based on the classical belief propagation algorithm, which has found wide success in classical coding theory when used in conjunction with LDPC or Turbo codes. More recently Rengaswamy et al. [2] numerically observed that BPQM implements the optimal decoder on a small example code, in that it implements the optimal measurement for distinguishing the quantum output states for the set of input codewords. Here we significantly expand the understanding, formalism, and applicability of the BPQM algorithm with the following contributions. First, we prove analytically that BPQM realizes optimal decoding for any binary linear code with tree Tanner graph. We also provide the first formal description of the BPQM algorithm in full detail and without any ambiguity. In so doing, we identify a key flaw overlooked in the original algorithm and subsequent works which implies quantum circuit realizations will be exponentially large in the code size. Although BPQM passes quantum messages, other information required by the algorithm is processed globally. We remedy this problem by formulating a truly messagepassing algorithm which approximates BPQM and has circuit complexity Oppoly n, polylog 1 ε q, where n is the code length and ε is the approximation error. Finally, we also propose a novel method for extending BPQM to factor graphs containing cycles by making use of approximate cloning. We show some promising numerical results that indicate that BPQM on factor graphs with cycles can significantly outperform the best possible classical decoder.

“…We assume such a conversion is implementable as a quantum gate and contained in f n . Actually, implementation of trigonometric functions and logarithm, which are necessary to the Box-Muller method, has been investigated in previous papers [13][14][15].…”

Section: A Our Ideamentioning

confidence: 99%

Reduction of Qubits in Quantum Algorithm for Monte Carlo Simulation by Pseudo-random Number Generator

Miyamoto,

Shiohara

2019

Preprint

It is known that quantum computers can speed up Monte Carlo simulation compared to classical counterparts. There are already some proposals of application of the quantum algorithm to practical problems, including quantitative finance. In many problems in finance to which Monte Carlo simulation is applied, many random numbers are required to obtain one sample value of the integrand, since those problems are extremely highdimensional integrations, for example, risk measurement of credit portfolio. This leads to the situation that the required qubit number is too large in the naive implementation where a quantum register is allocated per random number. In this paper, we point out that we can reduce qubits keeping quantum speed up if we perform calculation similar to classical one, that is, estimate the average of integrand values sampled by a pseudo-random number generator (PRNG) implemented on a quantum circuit. We present not only the overview of the idea but also concrete implementation of PRNG and application to credit risk measurement. Actually, reduction of qubits is a trade-off against increase of circuit depth. Therefore full reduction might be impractical, but such a trade-off between speed and memory space will be important in adjustment of calculation setting considering machine specs, if large-scale Monte Carlo simulation by quantum computer is in operation in the future.