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: QDD
X.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 operator
const n=#q;
// set n to length of input
int i; int j;
// declare loop counters
for 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