Quick Quantum Circuit Simulation

Abstract

Quick Quantum Circuit Simulation (QQCS) is a software system for computing the result of a quantum circuit using a notation that derives directly from the circuit, expressed in a single input line. Quantum circuits begin with an initial quantum state of one or more qubits, which are the quantum analog to classical bits. The initial state is modified by a sequence of quantum gates, quantum machine language instructions, to get the final state. Measurements are made of the final state and displayed as a classical binary result. Measurements are postponed to the end of the circuit because a quantum state collapses when measured and produces probabilistic results, a consequence of quantum uncertainty. A circuit may be run many times on a quantum computer to refine the probabilistic result. Mathematically, quantum states are 2n -dimensional vectors over the complex number field, where n is the number of qubits. A gate is a 2n ×2n unitary matrix of complex values. Matrix multiplication models the application of a gate to a quantum state. QQCS is a mathematical rendering of each step of a quantum algorithm represented as a circuit, and as such, can present a trace of the quantum state of the circuit after each gate, compute gate equivalents for each circuit step, and perform measurements at any point in the circuit without state collapse. Output displays are in vector coefficients or Dirac bra-ket notation. It is an easy-to-use educational tool for students new to quantum computing.

Hybrid Approaches for Efficient Simulations of 3-Qubit Quantum Fourier Transform (QFT) Circuit Using Quick Quantum Circuit Simulation (QQCS)

“…This section provides background information on quantum circuit simulation, decision diagrams, and property exploitation in simulations to keep this work self-contained. 1,2,3,4 The authors are the Department of Computer Engineering, Polytechnic University of the Philippines, E-mail: theamayenmalimban@gmail.com, kylereeceoropesa@iskolarngbayan.pup.edu.ph, czgeron@iskolarngbayan.pup.edu.ph and jkmcomia@iskolarngbayan.pup.edu.ph 5 The author is with the College of Engineering, Polytechnic University of the Philippines, E-mail: rgado@pup.edu.ph 6 The author is with the Research Institute for Strategic Foresight and Innovation, Polytechnic University of the Philippines, E-mail: odtubola@pup.edu.ph…”

“…In related work, Hillmich et al [2] introduced decision-diagram-based quantum circuit modeling, accelerating quantum circuit simulation on classical hardware. This representation method facilitates refined computations and reduces memory demands.…”

“…This study aimed to test a 3-qubit Quantum Fourier Transform (QFT) circuit consisting of a series of Hadamard, controlled, and SWAP gates. The researchers utilized Quick Quantum Circuit Simulation (QQCS) [2] as a computational tool to obtain the final quantum measurement of the circuit. QQCS operates by taking the linear sequence of gates in the circuit as input, starting with an initial state of |000 >, then applying the gates, and concluding with a final measurement.…”

“…Aside from the Reorder trick, quantum templates are also helpful in optimizing and synthesizing quantum circuits. Identifying a specific template to re-1 OPENQASM 2.0; 2 include "qelib1.inc"; 3 qreg q[3]; 4 creg meas [3]; 5 h q[0]; 6 cx q[0], q[1]; 7 cx q[1], q[2]; 8 h q[0]; 9 rz(pi/4) q[0]; 10 cx q[0], q [1]; 11 rz(-pi/4) q [1]; 12 cx q[0], q [1]; 13 rz(pi/4) q[1]; 14 h q [1]; 15 rz(pi/8) q[0]; 16 cx q[0], q [2]; 17 rz(-pi/8) q[2]; 18 cx q[0], q [2]; 19 rz(pi/8) q [2]; 20 rz(pi/4) q [1]; 21 cx q[1], q [2]; 22 rz(-pi/4) q [2]; 23 cx q[1], q [2]; 24 rz(pi/4) q [2]; 25 h q[2]; 26 barrier q[0], q[1], q [2]; 27 measure q[0] − > meas[0]; 28 measure q[1] − > meas [1]; 29 measure q[2] − > meas [2];…”

“…place rz(pi/8) q [2] in the circuit in Fig. 1, the researchers then identified additional templates using template identification in [6].…”