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  <title>Program — UChicago-UTokyo 1-day workshop on QI theory</title>
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      <div class="kicker">Program</div>
      <h1>UChicago-UTokyo 1-day workshop on QI theory — Program</h1>
      <p class="subtitle">All times Central Standard Time (CST). Click the cells to see abstract.</p>
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      <aside class="card">
        <h2>Overview</h2>
        <p>Talks are <strong>20 min</strong> + <strong>10 min Q&A</strong>.</p>
        <ul>
          <li>09:30 – Opening</li>
          <li>10:40 – Break</li>
          <li>12:10 – Lunch</li>
          <li>15:00 – Break</li>
          <li>17:00 – Closing</li>
          <li>17:30 – Dinner?</li>
        </ul>
      </aside>

      <section class="card">
        <h2>Detailed Timeline</h2>
        <ol class="timeline">
          <li class="slot">
            <div class="time">09:30–09:40</div>
            <div class="title">Opening Remarks & Introduction</div>
            <div class="small">Hosts</div>
          </li>

          <details class="slot">
            <summary>
              <div class="time">09:40–10:10</div>
              <div class="title">Soumik Ghosh</div>
              <div class="small">Quantum advantage with peaked circuits using error correction</div>
            </summary>
            <div class="abstract">
              Abstract
            </div>
          </details>

          <details class="slot">
            <summary>
              <div class="time">10:10–10:40</div>
              <div class="title">Yuki Koizumi</div>
              <div class="small">Faster Quantum Algorithm for Multiple Observables Estimation</div>
            </summary>
            <div class="abstract">
              Achieving quantum advantage in efficiently estimating collective properties of quantum many-body systems remains a fundamental goal in quantum computing.
While the quantum gradient estimation (QGE) algorithm has been shown to achieve doubly quantum enhancement in the precision and the number of observables, it remains unclear whether one benefits in practical applications. In this work, we present a generalized framework of the adaptive QGE algorithm, and further propose two variants which enable us to estimate the collective properties of fermionic systems using the smallest cost among existing quantum algorithms. The first method utilizes the symmetry inherent in the target state, and the second method enables estimation in a single-shot manner using the parallel scheme. We show that our proposal offers a quadratic speedup compared with prior QGE algorithms in the task of fermionic partial tomography for systems with limited particle numbers. Furthermore, we provide numerical demonstrations that, for a problem of estimating fermionic 2-RDMs, our proposals improve the number of queries to the target state preparation oracle by a factor of 4.4 for the nitrogenase FeMo cofactor and by a factor of 7.8 for Fermi-Hubbard model of 200 sites in chemical accuracy.
            </div>
          </details>

          <li class="slot break">
            <div class="time">10:40–11:10</div>
            <div class="title">Break</div>
            <div class="small">Coffee & discussion</div>
          </li>

          <details class="slot">
            <summary>
              <div class="time">11:10–11:40</div>
              <div class="title">Soichiro Imamura</div>
              <div class="small">Parallelization of Hadamard Test</div>
            </summary>
            <div class="abstract">
              The Hadamard Test is a fundamental quantum algorithm widely used in various quantum computing applications. It enables the estimation of the real or imaginary part of <ψ|U|ψ>, where |ψ> is a quantum state and U is a unitary operator. When applying the Hadamard Test to many different unitary operators, the number of distinct quantum circuits required increases accordingly, resulting in higher time and financial costs. In this work, we propose the Parallel Hadamard Test, which can replace any number of individual Hadamard Tests with a single quantum circuit. We demonstrate how this approach can be utilized in concrete examples, including the Variational Quantum Eigensolver (VQE), quantum phase estimation, and quantum kernel methods. For VQE, we also provide a cost comparison to highlight the efficiency gains achieved by our method. This unified approach significantly reduces the number of required quantum circuits, thereby lowering both computational time and financial costs.
            </div>
          </details>

          <details class="slot">
            <summary>
              <div class="time">11:40–12:10</div>
              <div class="title">James Sud</div>
              <div class="small">Classical Descriptions of Hamiltonian Optimization</div>
            </summary>
            <div class="abstract">
              The Local Hamiltonian Problem (LHP) is the canonical complete problem for QMA. We analyze three well-studied LHPs with only 2-local terms: Quantum MaxCut (QMC), XY, and EPR Hamiltonians. The first two are QMA-complete, the last is only known to be in StoqMA.

We show that all three Hamiltonians admit simple classical descriptions: for a given interaction graph G, we show that the Hamiltonians are equivalent to the spectra of the token graphs of G. We thus can directly apply results on the spectra radii of token graphs to understand the maximum energies of LHPs.

From numerical study, we conjecture new bounds for these spectral radii based on properties of G. We show how these conjectures tighten the analysis of existing algorithms, implying state-of-the-art approximation ratios for all three Hamiltonians. These LHPs are also equivalent to common models in statistical mechanics, such as the Heisenberg and XY models, so our conjectures also provide simple combinatorial bounds on the ground state energy of these models.
            </div>
          </details>

          <li class="slot lunch">
            <div class="time">12:10–13:30</div>
            <div class="title">Lunch Break</div>
            <div class="small">80 min</div>
          </li>

          <details class="slot">
            <summary>
              <div class="time">13:30–14:00</div>
              <div class="title">Rossoneri Jing</div>
              <div class="small">Quantum Error Correction of non-Abelian Anyons</div>
            </summary>
            <div class="abstract">
              Topological order (TO) provides a natural platform for storing and manipulating quantum information. However, its stability to noise has only been systematically understood for Abelian TOs. In this work, we exploit the non-deterministic fusion of non-Abelian anyons to inform active error correction and design decoders where the fusion products, instead of flag qubits, herald the noise. This intrinsic heralding enhances thresholds over those of Abelian counterparts when noise is dominated by a single non-Abelian anyon type. Furthermore, we use Bayesian inference to obtain a statistical mechanics model for fixed-point non-Abelian TOs with perfect measurements under any noise model, which yields the optimal threshold conditioned on measuring anyon syndromes. We numerically illustrate these results for $D_4 \cong \mathbb Z_4 \rtimes \mathbb Z_2$ TO. In particular, for non-Abelian charge noise and perfect syndrome measurement, we find a conditioned optimal threshold $p_c=0.218(1)$, whereas an intrinsically heralded minimal-weight perfect-matching (MWPM) decoder already gives $p_c=0.20842(2)$, outperforming standard MWPM with $p_c = 0.15860(1)$. Our work highlights how non-Abelian properties can enhance stability, rather than reduce it, and discusses potential generalizations for achieving fault tolerance.
            </div>
          </details>

          <details class="slot">
            <summary>
              <div class="time">14:00–14:30</div>
              <div class="title">Nobuyuki Yoshioka</div>
              <div class="small">Transversal gates for probabilistic implementation of multi-qubit Pauli rotations</div>
            </summary>
            <div class="abstract">
              We introduce a general framework for weak transversal gates -- probabilistic implementation of logical unitaries realized by local physical unitaries -- and propose a novel partially fault-tolerant quantum computing architecture that surpasses the standard Clifford+T architecture on workloads with million-scale Clifford+T gate counts. First, we prove the existence of weak transversal gates on the class of Calderbank-Shor-Steane codes, covering high-rate qLDPC and topological codes such as surface code or color codes, and present an efficient algorithm to determine the physical multi-qubit Pauli rotations required for the desired logical rotation. Second, we propose a partially fault-tolerant Clifford+ϕ architecture that performs in-place Pauli rotations via a repeat-until-success strategy; phenomenological simulations indicate that a rotation of 0.003 attains logical error of 9.5×10^{−5}  on a surface code with d=7 at physical error rate of 10^{−4}, while avoiding the spacetime overheads of magic state factories, small angle synthesis, and routing. Finally, we perform resource estimation on surface and gross codes for a Trotter-like circuit with N=108 logical qubits to show that the Clifford+ϕ architecture outperforms the conventional Clifford+T approach by a factor of tens to a hundred in runtime due to natural rotation-gate parallelism. This work open a novel paradigm for realizing logical operations beyond the constraints of conventional design.
            </div>
          </details>

          <details class="slot">
            <summary>
              <div class="time">14:30–15:00</div>
              <div class="title">Ryohei Weil</div>
              <div class="small">Quantum Phases of Matter on Hyperbolic Space</div>
            </summary>
            <div class="abstract">
             Quantum many-body systems on hyperbolic lattices have been a growing field of interest, with applications ranging from quantum gravity to error correction. Yet, fundamental connections between phases of matter, energetic structure, and correlations which are well-explored in Euclidean settings remain murky in the hyperbolic setting. In our work, we discuss insights gained from investigating the paradigmatic quantum transverse-field Ising model on the Cayley tree, using tensor networks as a central numerical and analytical tool. We also discuss how measurement and feedback may be able to efficiently prepare states on such lattices that have evaded constructions in Euclidean settings.
            </div>
          </details>

          <li class="slot break">
            <div class="time">15:00–15:30</div>
            <div class="title">Break</div>
            <div class="small">30 min</div>
          </li>

          <details class="slot">
            <summary>
              <div class="time">15:30–16:00</div>
              <div class="title">Atsushi Iwaki</div>
              <div class="small">Virtual Autopurification in Translationally Invariant Quantum States</div>
            </summary>
            <div class="abstract">
              We propose Virtual Autopurification (VAP), a new protocol for virtual purification of thermal or noisy quantum states, leveraging the translational invariance of physical systems. While conventional virtual purification requires multiple copies of the quantum state and global entangled measurements [1–3], our method eliminates this requirement by constructing virtual copies within a single translationally invariant system. Building on the concept of localized virtual purification [4], VAP performs entangled measurements between spatially distant subregions, effectively achieving virtual cooling with exponentially small errors in the inter-subregion distance. We theoretically show that VAP reproduces the results of localized virtual purification with exponential accuracy under the clustering property, and numerical simulations confirm the validity and efficiency of the method. Our results establish VAP as a practical and resource-efficient approach for thermal-state cooling and error mitigation in near-term quantum devices.
[1] J. Cotler, S. Choi, A. Lukin, H. Gharibyan, T. Grover, M. E. Tai, M. Rispoli, R. Schittko, P. M. Preiss, A. M. Kaufman, M. Greiner, H. Pichler, and P. Hayden, Phys. Rev. X 9, 031013 (2019).
[2] B. Koczor, Phys. Rev. X 11, 031057 (2021).
[3] W. J. Huggins, S. McArdle, T. E. O'Brien, J. Lee, N. C. Rubin, S. Boixo, K. B. Whaley, R. Babbush, and J. R. McClean, Phys. Rev. X 11, 041036 (2021).
[4] H. Hakoshima, S. Endo, K. Yamamoto, Y. Matsuzaki, and N. Yoshioka, Phys. Rev. Lett. 133, 080601 (2024).
            </div>
          </details>

          <details class="slot">
            <summary>
              <div class="time">16:00–16:30</div>
              <div class="title">Mahadevan Subramanian</div>
              <div class="small">Achievable rates for concatenated square Gottesman-Kitaev-Preskill (GKP) codes</div>
            </summary>
            <div class="abstract">
              The Gottesman-Kitaev-Preskill (GKP) codes are known to achieve optimal rates under displacement noise and pure loss channels, which establishes theoretical foundations for its optimality. However, such optimal rates are only known to be achieved at a discrete set of noise strength with the current self-dual symplectic lattice construction. In this work, we develop a new coding strategy using concatenated continuous variable - discrete variable encodings to go beyond past results and establish GKP's optimal rate over all noise strengths. In particular, for displacement noise, the rate is obtained through a constructive approach by concatenating GKP codes with a quantum polar code and analog decoding. For pure loss channel, we prove the existence of capacity-achieving GKP codes through a random coding approach. These results highlight the capability of concatenation-based GKP codes and provides new methods for constructing good GKP lattices.
            </div>
          </details>

          <details class="slot">
            <summary>
              <div class="time">16:30–17:00</div>
              <div class="title">Su-un Lee</div>
              <div class="small">Efficient benchmarking of logical magic state</div>
            </summary>
            <div class="abstract">
              High-fidelity logical magic states are a critical resource for fault-tolerant quantum computation, enabling non-Clifford logical operations through state injection. However, benchmarking these states presents significant challenges: one must estimate the infidelity $\epsilon$ with multiplicative precision, while many quantum error-correcting codes only permit Clifford operations to be implemented fault-tolerantly. Consequently, conventional state tomography requires $\sim1/\epsilon^2$ samples, making benchmarking impractical for high-fidelity states. In this work, we show that any benchmarking scheme measuring one copy of the magic state per round necessarily requires $\Omega(1/\epsilon^2)$ samples for single-qubit magic states. We then propose two approaches to overcome this limitation: (i) Bell measurements on two copies of the twirled state and (ii) single-copy schemes leveraging twirled multi-qubit magic states. Both benchmarking schemes utilize measurements with stabilizer states orthogonal to the ideal magic state and we show that $O(1/\epsilon)$ sample complexity is achieved, which we prove to be optimal. Finally, we demonstrate the robustness of our protocols through numerical simulations under realistic noise models, confirming that their advantage persists even at moderate error rates currently achievable in state-of-the-art experiments.
            </div>
          </details>

          <li class="slot lunch">
            <div class="time">After workshop</div>
            <div class="title">Spontaneous Dinner</div>
          </li>

        </ol>

        <p class="small">Program subject to minor adjustments.</p>
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