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Simulation of Mixed Qubit-Qumode Circuits for Variational Algorithms

Blake Burgstahler

Advisor: Frank Mueller

Operations Research PhD Student

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Gate Based Quantum

  • Quantum Gates (and Circuits) can be expressed as a matrix

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Selected CV-DV Background

  • Qubit Encoding
    • Discrete Variables
    • 2-level
  • Fock Encoding
    • Discrete Variables
    • n-level: Photon count
  • Phase-Space Encoding
    • Continuous Variables
    • Position (x) & Momentum (p)

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Why use qumodes?

  • Naturally allows for mixing of continuous and discrete variables
    • Optimization problems in either space
  • Encoding Density
    • many-qubit -> single-qumode
  • Potential for improved fidelity
    • Unique operators
    • Isolated noise sources (hardware dependant)
  • Various hardware schemes
    • Superconducting, Trapped Ion, Neutral Atom

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Quantum Approx. Optimization Algorithm

  • Each iteration has 2 parameters which are classically optimized

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https://medium.com/@chs.li.work/qaoa-quantum-approximate-optimization-algorithm-1cf6dabdd581

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NchooseK (NCK)

  • Constraint satisfaction programming
    • “Given set of Boolean variables N, exactly K of must be true”
    • Hard and Soft constraints
  • Easily adaptable to many classes of problems
    • 3-SAT, maximum cut, map coloring, minimum vertex cover, etc.

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"Combining Hard and Soft Constraints in Quantum Constraint-Satisfaction Systems," in SC22

"Mapping Constraint Problems onto Quantum Gate and Annealing Devices," 2021 QCS

"Implementing NChooseK on IBM Q Quantum Computer Systems,” RC 2019

Minimum Vertex Cover

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Extending NchooseK

NchooseK constraints

QUBO

Quantum annealers

(using D-Wave’s Ocean)

Circuit-model quantum computers

(using IBM’s Qiskit)

Classical computers (using Microsoft’s Z3 SMT solver)

(via QAOA)

 

Bosonic Model

(using simulation,

Xanadu? Pasqal?)

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Bosonic-Qiskit

  • C2QA’s extension to Qiskit
    • Add Qumode computational capabilities
    • Nearly identical circuit construction
    • Execute with Qiskit Simulators

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Some Ansatzes and Targets

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Qubit QAOA

Qumode QAOA

(not full circuit)

Hybrid VQE

(6 repetitions)

Qiskit - Baseline

Simulation -

Design Ansatz w/ hardware in mind

“Fast universal control of an oscillator with weak dispersive coupling to a qubit” Nature Physics 2022

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Bosonic-Qiskit vs Custom Simulator

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​

Bosonic-Qiskit

Circuit Object

C2qa.CVCircuit

(extends Qiskit.Circuit)

Register Features

Qubits only

(2n Fock levels)

Prep for Simulation

Transpilation (slow!)

Simulator

Qiskit Aer

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Convert

Circuit Execution

  • Convert up to 20x faster than Transpilation up 212 level systems
  • Total simulation time similar at these scales

Custom Simulator

HybridCircuit

(extends Qiskit.Circuit)

Arbitrary Fock Levels

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None needed

(directly use matrices)

Matrix-Vector Multiply

(Dense or Sparse)

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In Progress and Future Work

  • Improving scalability (w/ Srikar)
    • Circumvent conversion (write directly w/ HybridCircuit syntax)
    • DiaQ backend instead of naïve dense
    • Alternate problem encodings
    • Mapping across multiple qumodes
  • Comparisons against Qubit-only based approaches
    • Simulation: Noise-free; add noisy simulation
    • Hardware: Surveying options. Xandu? Pascal? Others?

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Questions?

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