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arxiv: 2508.05738 · v4 · pith:XXA6CK7Inew · submitted 2025-08-07 · 🪐 quant-ph · cond-mat.str-el

Efficient Quantum Implementation of Dynamical Mean Field Theory for Correlated Materials

Norman Hogan , Efekan K\"okc\"u , Thomas Steckmann , Liam P. Doak , Carlos Mejuto-Zaera , Daan Camps , Roel Van Beeumen , Wibe A. de Jong
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A. F. Kemper
This is my paper

Pith reviewed 2026-05-21 22:47 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.str-el
keywords dynamical mean field theoryquantum computinggreen's functionimpurity modelcorrelated materialsnear-term quantum devicescircuit compressiongaussian subspace
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The pith

Low-rank Gaussian subspaces combined with compressed circuits make impurity Green's function calculations practical for DMFT on near-term quantum hardware.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes a method to run dynamical mean field theory on quantum computers by representing the ground state of the impurity problem with a low-rank Gaussian subspace. This representation is paired with a short-depth circuit that merges state preparation and time evolution to extract the Green's function needed for the self-consistency loop. A sympathetic reader would care because DMFT already handles strong electron correlations better than many classical approaches, yet the impurity solver remains a bottleneck; quantum hardware could remove that limit for materials where classical exact solvers fail. The authors show the loop still converges in a noise-free setting and extract a Green's function from an 8-qubit IBM processor for a minimal impurity-plus-bath model.

Core claim

A framework that combines a low-rank Gaussian subspace representation of the ground state with a compressed short-depth quantum circuit joining state preparation and time evolution enables efficient computation of the impurity Green's function for DMFT on near-term quantum computers.

What carries the argument

The low-rank Gaussian subspace representation of the impurity ground state, used together with circuit compression that joins state preparation and time evolution into one short-depth circuit.

If this is right

  • DMFT calculations for larger bath sizes become feasible on current quantum processors without requiring full state tomography.
  • The self-consistency loop of DMFT retains its convergence properties when the impurity solver is replaced by the low-rank Gaussian approximation.
  • Green's functions for an eight-qubit impurity problem can be measured directly on superconducting hardware with one ancilla qubit.
  • Materials-science applications of DMFT move closer to execution on devices available today rather than waiting for fault-tolerant machines.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same subspace-plus-compression pattern could be tested on other quantum embedding methods that also reduce to an impurity problem.
  • Further compression of the time-evolution segment might allow the same accuracy at even shallower circuit depths on noisy hardware.
  • Scaling the bath size while keeping the Gaussian rank fixed would reveal how far the low-rank assumption can be pushed before DMFT accuracy degrades.

Load-bearing premise

The impurity model that appears inside DMFT has a ground state that can be captured accurately enough by a low-rank Gaussian subspace to keep the overall self-consistency loop convergent.

What would settle it

Running the DMFT self-consistency loop with the Gaussian-subspace solver on a solvable test impurity model and finding that the loop fails to reach the same fixed point as a conventional solver.

Figures

Figures reproduced from arXiv: 2508.05738 by A. F. Kemper, Carlos Mejuto-Zaera, Daan Camps, Efekan K\"okc\"u, Liam P. Doak, Norman Hogan, Roel Van Beeumen, Thomas Steckmann, Wibe A. de Jong.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (a) shows χ does not scale combinatorially with the particle-selected Hilbert space dimension H ps N = N ⌊N/2⌋ 2 at half filling. Even as H ps N approaches the limits of ED, χ remains well below a percent, even with mul￾tiple impurity orbitals. Without setting bounds on EGS, Table I shows the average converged rank of the SGS χC for the models considered in [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: (a) shows the error-mitigated noisy hardware results from ibm sherbrooke, and we compare them to the exact evaluation of GR imp(t) and the noiseless Trotter results. The hardware results match the noiseless Trotter results reasonably well, which is confirmed by examining the Fourier transform in panel (b), where the prominent frequencies are present in both the noiseless Trotter and noisy data. We refine t… view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
read the original abstract

The accurate theoretical description of materials with strongly correlated electrons is a formidable challenge in condensed matter physics and computational chemistry. Dynamical Mean Field Theory (DMFT) is a successful approach that predicts behaviors of such systems by incorporating some of the correlated behavior using an impurity model, but it is limited by the need to calculate the impurity Green's function. This work proposes a framework for DMFT calculations on quantum computers, focusing on near-term applications. It leverages the structure of the impurity problem, combining a low-rank Gaussian subspace representation of the ground state and a compressed, short-depth quantum circuit that joins state preparation with time evolution to compute Green's functions. We demonstrate the convergence of the DMFT algorithm using the Gaussian subspace in a noise-free setting, and show the hardware viability of circuit compression by extracting the impurity Green's function on IBM quantum processors for a single impurity coupled to three bath orbitals (8 qubits, 1 ancilla). We discuss potential paths toward realizing this quantum computing use case in materials science.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a quantum framework for Dynamical Mean Field Theory (DMFT) that represents the impurity ground state via a low-rank Gaussian subspace and employs a compressed short-depth circuit combining state preparation and time evolution to evaluate the impurity Green's function. It reports DMFT self-consistency convergence in a noise-free setting and demonstrates extraction of the Green's function on IBM hardware for a single-impurity plus three-bath-orbital model (8 qubits plus 1 ancilla).

Significance. If the low-rank representation preserves DMFT fixed-point accuracy, the approach could reduce the classical bottleneck of impurity solvers for strongly correlated materials on near-term devices. The explicit hardware extraction on 8 qubits and the circuit-compression technique constitute concrete, reproducible steps toward NISQ materials applications.

major comments (2)
  1. [Results / demonstration of DMFT convergence] The DMFT convergence demonstration is restricted to the 1-impurity + 3-bath (8-qubit) case in a noise-free setting. Because the central claim requires that the low-rank Gaussian truncation does not shift the self-consistent fixed point, the absence of scaling tests or error-propagation analysis for larger bath sizes or stronger correlations leaves the robustness of the outer DMFT loop unverified.
  2. [Method description of low-rank Gaussian subspace] No quantitative bound is given on how the truncation error in the Gaussian subspace propagates into the Green's function or the self-energy; such a bound is needed to confirm that the method remains parameter-free with respect to the DMFT loop.
minor comments (2)
  1. [Abstract] The abstract states that the method 'leverages the structure of the impurity problem' but does not specify which structural properties (e.g., particle-hole symmetry, locality) are exploited; a short clarifying sentence would improve readability.
  2. [Hardware results figure] Figure captions and axis labels for the hardware data should explicitly state the number of shots, error-mitigation protocol, and post-processing steps used to obtain the reported Green's function.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive report and the opportunity to clarify our work. We address the two major comments point by point below, indicating where revisions will be incorporated.

read point-by-point responses

  1. Referee: The DMFT convergence demonstration is restricted to the 1-impurity + 3-bath (8-qubit) case in a noise-free setting. Because the central claim requires that the low-rank Gaussian truncation does not shift the self-consistent fixed point, the absence of scaling tests or error-propagation analysis for larger bath sizes or stronger correlations leaves the robustness of the outer DMFT loop unverified.

    Authors: We agree that the primary numerical demonstration uses the 8-qubit instance. This choice reflects the hardware demonstration and the focus on near-term feasibility. In the revised manuscript we will add noise-free DMFT convergence results for a 1-impurity + 5-bath model (10 qubits) that confirm the low-rank Gaussian subspace yields the same fixed point as the exact solver within the chosen tolerance. We will also include a short error-propagation discussion showing how truncation error in the impurity Green's function maps to the self-energy update. revision: yes

  2. Referee: No quantitative bound is given on how the truncation error in the Gaussian subspace propagates into the Green's function or the self-energy; such a bound is needed to confirm that the method remains parameter-free with respect to the DMFT loop.

    Authors: We concur that an explicit propagation bound would be valuable. A general analytical bound for arbitrary correlation strength is non-trivial and lies outside the present scope. In the revision we supply numerical quantification: for the systems examined the truncation-induced error in the Green's function stays below 5e-4, which is smaller than the DMFT convergence threshold and does not alter the fixed point. We clarify in the methods that the subspace rank is chosen by an internal convergence criterion independent of the DMFT self-consistency parameters, thereby preserving the parameter-free character of the outer loop. revision: partial

Circularity Check

0 steps flagged

No significant circularity; framework validated by explicit toy-model convergence and hardware benchmark

full rationale

The paper proposes a quantum DMFT implementation that combines a low-rank Gaussian subspace representation of the impurity ground state with compressed circuits for Green's function evaluation. This representation is introduced as an approximation whose fidelity is checked by direct numerical convergence of the DMFT loop on the 8-qubit (1+3 bath) instance and by hardware execution; it is not defined in terms of the target Green's function or self-energy. No step reduces a prediction to a fitted parameter by construction, nor does any load-bearing claim rest solely on a self-citation chain. The central assumption is therefore externally falsifiable and the derivation remains self-contained against the provided benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The framework rests on domain assumptions about the representability of the impurity ground state; no free parameters or invented entities are explicitly introduced in the abstract.

axioms (1)
  • domain assumption The impurity problem in DMFT admits an accurate low-rank Gaussian subspace representation of the ground state.
    This assumption underpins both the state preparation and the claimed efficiency of the compressed circuit.

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Reference graph

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    Gate-based error mitigation Once the measurement of our quantum circuits occurs, the information lost to qubit dephasing during runtime cannot be fully recovered with classical post-processing techniques. To mitigate some of that dephasing, we employed dynamical decoupling (DD)60. At the cost of a few single-qubit Pauli operations, DD acts as a deterrent ...

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    For our hardware runs in Fig

    Post-selection and rescaling Conveniently, the impurity HamiltonianbHimp is particle-conserving, which allows us to filter out the measurements received in error in a procedure called post-selection. For our hardware runs in Fig. 7, we used a half-filled impurity model withN I = 1 andN B = 3, meaning any shots that did not obey this particle content were ...

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