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Programming Languages for
Quantum Computing
“Just the High (qu)Bits”
Vadim von Brzeski
[email protected]
CS 203
QRAM Model of QC
Classical Control, Quantum Data
Quantum Subsystem
(QRAM)
Sequence of Operations
Classical
Control
System
qureg
Measurement
Typical Sequence of a Quantum Computation :
1. Initialize quantum subsystem
2. Perform sequence of operations (transformations)
3. Measure the result (one or more qubits)
4. Is the result correct ? No – Goto to Step 1.
register(s) of
n qubits in
quantum
superposition
of all 2n
possible states
Constraints on a Quantum Program
qubit q, p;
bit b, c;
...
q := p;
...
...
b := p && p;
quantum_op (p, p);
...
...
c := p;
quantum_op(p);
....
....
quantum_op(q);
All operations on quantum
states must be reversible.
No-cloning rule : cannot copy a quantum
system that is in an unknown state.
Operations must be on distinct states.
Copy-by-value not allowed.
An implicit measurement of qubit p.
Collapses the quantum state of p
(side-effect). quantum_op(p) will not
yield expected result.
If p and q are in an entangled quantum
state, measuring p above also affects q.
How do you ensure a quantum program is well-formed and well-typed ?
Two Camps
• Formalists
– Define formal semantics and type systems for QPLs
• Semantics of non-deterministic programs
– “weakest precondition”  “greatest pre-expectation”
– Quantum lambda calculi
– Functional language domain
– Focus on static checking
• Pragmatists
– Quantum simulators on classical computers
– Extensions of popular imperative and functional
languages
• C++
• Haskell
– Run-time checking
Two Examples
• Quantum Lambda Calculus (van Tonder)
– Based on theory of linear lambda calculi
Non-linear terms
– e :: = x | λx.e | e e | !e | λ!x.e
– Linear term may appear in a function body exactly once
• (λx. (x x)) is not valid since x is a linear term
• Reversible Computation (Sanders & Zuliani, qGCL)
– Set of rules (compiler) for transforming non-reversible
programs to reversible programs
x := e
push x;
x := e;
pop x;