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Electron-Phonon Systems on a Universal Quantum Computer
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Electron-Phonon Systems on a Universal Quantum Computer
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We present an algorithm that extends existing quantum algorithms for simulating fermion systems in quantum chemistry and condensed matter physics to include bosons in general and phonons in particular. We introduce a qubit representation for the low-energy subspace of phonons which allows an efficient simulation of the evolution operator of the electron-phonon systems. As a consequence of the Nyquist-Shannon sampling theorem, the phonons are represented with exponential accuracy on a discretized Hilbert space with a size that increases linearly with the cutoff of the maximum phonon number. The additional number of qubits required by the presence of phonons scales linearly with the size of the system. The additional circuit depth is constant for systems with finite-range electron-phonon and phonon-phonon interactions and linear for long-range electron-phonon interactions. Our algorithm for a Holstein polaron problem was implemented on an Atos Quantum Learning Machine (QLM) quantum simulator employing the Quantum Phase Estimation method. The energy and the phonon number distribution of the polaron state agree with exact diagonalization results for weak, intermediate and strong electron-phonon coupling regimes.
Forward citations
Cited by 7 Pith papers
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Tightening energy-based boson truncation bound using Monte Carlo-assisted methods
A Monte Carlo-assisted analytic method tightens energy-based bounds on boson truncation errors, substantially reducing the volume dependence of the required cutoff in scalar and gauge theories.
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Tightening energy-based boson truncation bound using Monte Carlo-assisted methods
Monte Carlo-assisted tightening of the energy-based boson truncation bound substantially reduces volume dependence in (1+1)D scalar field theory and (2+1)D U(1) gauge theory.
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Fault-Tolerant Resource Comparison of Qudit and Qubit Encodings for Diagonal Quadratic Operators
Qudit encodings for quadratic diagonal evolutions require exponentially stronger synthesis advantages than qubits to win asymptotically in product formulas but can yield constant-factor savings in LCU at low d.
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Fault-Tolerant Resource Comparison of Qudit and Qubit Encodings for Diagonal Quadratic Operators
For diagonal quadratic evolutions, qubit encodings are asymptotically cheaper than qudit encodings in both Trotter and LCU settings, but small-dimension qudits can win under favorable synthesis or code-switching assumptions.
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Exponentially improved quantum simulation of scalar QFT
Diagonalizing field operators before Pauli-string decomposition exponentially cuts circuit depth and Trotter errors in 2+1D scalar QFT simulations, with faster local-truncation convergence for Lorentzian energy-energy...
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Fault-Tolerant Resource Comparison of Qudit and Qubit Encodings for Diagonal Quadratic Operators
The paper derives explicit finite-d break-even synthesis costs for qudit vs. qubit encodings of diagonal quadratic operators in product-formula and LCU simulations, identifying low-d regions where qudits yield savings.
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Tightening energy-based boson truncation bound using Monte Carlo-assisted methods
New analytic and Monte Carlo-assisted method tightens energy-based boson truncation bounds, reducing volume dependence in (1+1)D scalar and (2+1)D U(1) gauge theories.
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