Quantum Simulators

DoRon Motter

August 2, 2001

Introduction

• Currently a wide variety of quantum simulators are available

• Good to know to avoid duplication of effort

• Different simulators have different target audiences

• Different simulators have different strengths/weaknesses

Simulator Space

• Simulators of a single algorithm– ex. Shor’s Algorithm

• Simulators for illustration– Often simulate a single algorithm– Give some sort of display with heavily

annotated source

• Quantum API’s / Programming Languages• Java Applets

Single Algorithm

• Often provide the best performance (for this single algorithm)

• Performance results vary– Different ‘implementations’ of the algorithm– Different OS/language requirements– Different results(!)

• Often undeveloped API’s

Illustrative Simulators

• Often Mathematica worksheets

• Provide heavily annotated source

• Often integrate source/annotations and display

• Useful when attempting to understand (or explain)

Quantum API’s

• Provide ‘high-level’ quantum operations

• Often provide completely generic QC simulation

• The widest approach, with several good options

Simulator Traits

• Interface – C/C++– GUI

• Speed

• Source Availability

• Universality

Single Algorithm: OpenQubit

• http://www.ennui.net/~quantum/

• API but only complete enough to do Shor’s

• Open Source (GPL)

• Useful because it’s GPL and hopes to become an API

Quantum API: QCE

• http://rugth30.phys.rug.nl/compphys0/qce.htm

• Quantum Computer Emulator• Provides support (GUI) for testing/sim of quantum

algorithms on various hardware – Support for interactions as a result of implementation

• Interesting because it takes into account physical implementation

• Built in visualization

Quantum API: QCE

Quantum API: QDD

• http://home.plutonium.net/~dagreve/qdd.html• (And SHORNUF…)• Uses BDD’s to represent quantum state

– Gains an efficiency advantage

– Loses the ability to perform analog computations

• Open Source• Probably the most efficient ‘general purpose’

simulator

Quantum API: QDDX.Set(0); // place the register in a superposition of states.X.Mix();F.Set(0);expn(A,Number,X,F, 1); // F = a^X mod n // Perform a classical sampling of F. This collapses the entire

quantum // state so that it is consistant with the value measured in F. Fv = F.Sample(); // Measure the period of X. Unfortunately, a bit of a quantum cheat.Pv = X.Period();f1 = gcd((powmod(A,Pv/2,Number) + 1) % Number , Number) ;f2 = gcd((powmod(A,Pv/2,Number) + Number - 1) % Number ,

Number) ;Xv = X.Sample(); Cv = powmod(A,Xv,Number); assert(Cv == Fv, "Mismatch"); f1 = gcd(Number,f1); f2 = gcd(Number,f2); Factor = (f1 > f2 ? f1 : f2); found = (Factor > 1) && (Factor < Number);

Quantum API: QCL

• http://tph.tuwien.ac.at/~oemer/qcl.html

• Quantum Computation Language

• A high-level, architecture independent programming language

• Separates algorithm from implementation

• Provides reference implementation

• Interprets commands in its own ‘shell’

Quantum API: QCL

operator dft(qureg q) { // main operatorconst n=#q; // set n to length of inputint i; int j; // declare loop countersfor i=0 to n-1 {

for j=0 to i-1 { // apply conditional phase gates

CPhase(2*pi/2^(i-j+1),q[n-i-1] & q[n-j-1]);}Mix(q[n-i-1]); // qubit rotation

}flip(q); // swap bit order of the output

}

Quantum API: QCS

• http://www.senko-corp.co.jp/qcs/

• Universal Quantum Computer Simulator

• Closed Source, Commercial

• GUI interface to building circuits

Conclusion

• Different approaches to Universality– GUI circuit building from gates– C++ algorithm writing

• Tradeoffs must be considered– Universality vs. Speed