Simulation of Quantum Computations in Lisp Brecht Desmet, Ellie - - PowerPoint PPT Presentation

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Jan 03, 2024 144 likes •223 views

Simulation of Quantum Computations in Lisp Brecht Desmet, Ellie DHondt, Pascal Costanza, and Theo DHondt 1 Quantum computations Computation below the level of atoms Postulates of quantum mechanics Qubits Superposition

SLIDE 1

Simulation of Quantum Computations in Lisp

Brecht Desmet, Ellie D’Hondt, Pascal Costanza, and Theo D’Hondt

SLIDE 2

Quantum computations

Computation below the level of atoms
Postulates of quantum mechanics
Qubits
Superposition
Entanglement
Measurement
Quantum operators
Unitary evolution
Quantum parallelism
Quantum algorithms
Shor’s algorithm

SLIDE 3

Quantum Simulator

Why?
Lack of existing general-purpose machines
Perform experiments
That go beyond postulates of quantum mechanics
Instrument for communication between

interdisciplinary research

Problem?
Simulation on classical machine has an

inherently exponential complexity

SLIDE 4

QLisp in a nutshell

Simulation as a model
Thinking in terms of mathematical concepts
Overrule postulates of quantum mechanics
Modify quantum states
Compact expressive language
Macro extension of Lisp
Education opportunities
Software optimizations
Prune time and space complexity for small problems

SLIDE 5

Algorithm of Deutsch-Jozsa

(defun deutsch-jozsa (n unitary-fn)

"returns T if unitary-fn is constant” (let* ((_phi1_ (make-qureg n (hadamard-init))) (_phi2_ (qc-apply (make-qureg 1 (standard-init 1)) (-h-))) (_psi_ (funcall unitary-fn (tensor-items _phi1_ _phi2_)))) (constant-qureg-p (collapse-basis (qc-apply-range _psi_ -h- 0 (1- n))))))

SLIDE 6