Publications
Our teams aspire to make discoveries that impact everyone, and core to our approach is sharing our research and tools to fuel progress in the field.
Our teams aspire to make discoveries that impact everyone, and core to our approach is sharing our research and tools to fuel progress in the field.
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1 - 15 of 139 publications
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The solution of linear systems of equations is the basis of many other quantum algorithms, and recent results provided an algorithm with optimal scaling in both the condition number κ and the allowable error ϵ [PRX Quantum 3, 0403003 (2022)]. That work was based on the discrete adiabatic theorem, and worked out an explicit constant factor for an upper bound on the complexity. Here we show via numerical testing on random matrices that the constant factor is in practice about 1,200 times smaller than the upper bound found numerically in the previous results. That means that this approach is far more efficient than might naively be expected from the upper bound. In particular, it is over an order of magnitude more efficient than using a randomized approach from [arXiv:2305.11352] that claimed to be more efficient.
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Given copies of a quantum state $\rho$, a shadow tomography protocol aims to learn all expectation values from a fixed set of observables, to within a given precision $\epsilon$. We say that a shadow tomography protocol is \textit{triply efficient} if it is sample- and time-efficient, and only employs measurements that entangle a constant number of copies of $\rho$ at a time. The classical shadows protocol based on random single-copy measurements is triply efficient for the set of local Pauli observables. This and other protocols based on random single-copy Clifford measurements can be understood as arising from fractional colorings of a graph $G$ that encodes the commutation structure of the set of observables. Here we describe a framework for two-copy shadow tomography that uses an initial round of Bell measurements to reduce to a fractional coloring problem in an induced subgraph of $G$ with bounded clique number. This coloring problem can be addressed using techniques from graph theory known as \textit{chi-boundedness}. Using this framework we give the first triply efficient shadow tomography scheme for the set of local fermionic observables, which arise in a broad class of interacting fermionic systems in physics and chemistry. We also give a triply efficient scheme for the set of all $n$-qubit Pauli observables. Our protocols for these tasks use two-copy measurements, which is necessary: sample-efficient schemes are provably impossible using only single-copy measurements. Finally, we give a shadow tomography protocol that compresses an $n$-qubit quantum state into a $\poly(n)$-sized classical representation, from which one can extract the expected value of any of the $4^n$ Pauli observables in $\poly(n)$ time, up to a small constant error.
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Quartic Quantum Speedups for Planted Inference Problems
Alexander Schmidhuber
Ryan O'Donnell
Physical Review X, 15 (2025), pp. 021077
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We describe a quantum algorithm for the Planted Noisy kXOR problem (also known as sparse Learning Parity with Noise) that achieves a nearly quartic (4th power) speedup over the best known classical algorithm while also only using logarithmically many qubits. Our work generalizes and simplifies prior work of Hastings, by building on his quantum algorithm for the Tensor Principal Component Analysis (PCA) problem. We achieve our quantum speedup using a general framework based on the Kikuchi Method (recovering the quartic speedup for Tensor PCA), and we anticipate it will yield similar speedups for further planted inference problems. These speedups rely on the fact that planted inference problems naturally instantiate the Guided Sparse Hamiltonian problem. Since the Planted Noisy kXOR problem has been used as a component of certain cryptographic constructions, our work suggests that some of these are susceptible to super-quadratic quantum attacks.
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Optimization by Decoded Quantum Interferometry
Stephen Jordan
Noah Shutty
Mary Wootters
Alexander Schmidhuber
Robbie King
Sergei Isakov
Nature (2025)
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Achieving superpolynomial speed-ups for optimization has long been a central goal for quantum algorithms. Here we introduce decoded quantum interferometry (DQI), a quantum algorithm that uses the quantum Fourier transform to reduce optimization problems to decoding problems. When approximating optimal polynomial fits over finite fields, DQI achieves a superpolynomial speed-up over known classical algorithms. The speed-up arises because the algebraic structure of the problem is reflected in the decoding problem, which can be solved efficiently. We then investigate whether this approach can achieve a speed-up for optimization problems that lack an algebraic structure but have sparse clauses. These problems reduce to decoding low-density parity-check codes, for which powerful decoders are known. To test this, we construct a max-XORSAT instance for which DQI finds an approximate optimum substantially faster than general-purpose classical heuristics, such as simulated annealing. Although a tailored classical solver can outperform DQI on this instance, our results establish that combining quantum Fourier transforms with powerful decoding primitives provides a promising new path towards quantum speed-ups for hard optimization problems.
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Rapid Initial-State Preparation for the Quantum Simulation of Strongly Correlated Molecules
Dominic Berry
Yu Tong
Alec White
Tae In Kim
Lin Lin
Seunghoon Lee
Garnet Chan
PRX Quantum, 6 (2025), pp. 020327
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Studies on quantum algorithms for ground-state energy estimation often assume perfect ground-state preparation; however, in reality the initial state will have imperfect overlap with the true ground state. Here, we address that problem in two ways: by faster preparation of matrix-product-state (MPS) approximations and by more efficient filtering of the prepared state to find the ground-state energy. We show how to achieve unitary synthesis with a Toffoli complexity about 7 × lower than that in prior work and use that to derive a more efficient MPS-preparation method. For filtering, we present two different approaches: sampling and binary search. For both, we use the theory of window functions to avoid large phase errors and minimize the complexity. We find that the binary-search approach provides better scaling with the overlap at the cost of a larger constant factor, such that it will be preferred for overlaps less than about 0.003. Finally, we estimate the total resources to perform ground-state energy estimation of Fe-S cluster systems, including the FeMo cofactor by estimating the overlap of different MPS initial states with potential ground states of the FeMo cofactor using an extrapolation procedure. With a modest MPS bond dimension of 4000, our procedure produces an estimate of approximately 0.9 overlap squared with a candidate ground state of the FeMo cofactor, producing a total resource estimate of 7.3e10 Toffoli gates; neglecting the search over candidates and assuming the accuracy of the extrapolation, this validates prior estimates that have used perfect ground-state overlap. This presents an example of a practical path to prepare states of high overlap in a challenging-to-compute chemical system.
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Diamond Circuits for Surface Codes
arXiv (2025)
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This short paper describes a new circuit to measure surface codes, which allows them to be implemented on the heavy-square lattice. The circuits perform far worse than the usual surface code, but are more efficient in terms of the distance they can achieve for a given number of qubits and couplers.
Paper Abstract:
We present and benchmark an interesting subfamily of circuits within the LUCI framework, which we refer to as diamond circuits, that implement a surface code on a Lieb or “Heavy-Square” lattice. This makes them more qubit- and measurement-efficient than previous constructions. These circuits are built around a mid-cycle state that resembles a Bravyi-Bacon-Shor surface code on the data and measurement qubits. These circuits preserve the spacelike distance of the code, but suffer a penalty in timelike distance. This could be useful in regimes where quantum computers are limited by the number of control lines or frequency collisions.
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Preview abstract
Protecting user privacy in financial transactions is desirable, yet in the classical world it is effectively impossible without hardware assumptions. Most existing quantum money schemes also fail to guarantee anonymity. We introduce a construction of single-use quantum tokens that give users the ability to detect whether the issuing authority is tracking them, for which we prove unconditional security. Our tokens do not require quantum communication from the users themselves, making them relatively practical to deploy.
We discuss potential applications including one-time payment tokens, anonymous one-time pads and voting.
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Faster electronic structure quantum simulation by spectrum amplification
Guang Hao Low
Robbie King
Alec White
Rolando Somma
Dominic Berry
Qiushi Han
Albert Eugene DePrince III
arXiv (2025) (to appear)
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We discover that many interesting electronic structure Hamiltonians have a compact and close-to-frustration-free sum-of-squares representation with a small energy gap. We show that this gap enables spectrum amplification in estimating ground state energies, which improves the cost scaling of previous approaches from the block-encoding normalization factor $\lambda$ to just $\sqrt{\lambda E_{\text{gap}}}$. For any constant-degree polynomial basis of fermionic operators, a sum-of-squares representation with optimal gap can be efficiently computed using semi-definite programming. Although the gap can be made arbitrarily small with an exponential-size basis, we find that the degree-$2$ spin-free basis in combination with approximating two-body interactions by a new Double-Factorized (DF) generalization of Tensor-Hyper-Contraction (THC) gives an excellent balance of gap, $\lambda$, and block-encoding costs. For classically-hard FeMoco complexes -- candidate applications for first useful quantum advantage -- this combination improves the Toffoli gates cost of the first estimates with DF [Phys. Rev. Research 3, 033055] or THC [PRX Quantum 2, 030305] by over two orders of magnitude.
https://drive.google.com/file/d/1hw4zFv_X0GeMpE4et6SS9gAUM9My98iJ/view?usp=sharing
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Tesseract: A Search-Based Decoder for Quantum Error Correction
Laleh Beni
Oscar Higgott
Noah Shutty
2025
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Tesseract is a Most-Likely-Error decoder designed for quantum error-correcting codes. Tesseract conducts a search through an graph on the set of all subsets of errors to find the lowest cost subset of errors consistent with the input syndrome. Although this set is exponentially large, the search can be made efficient in practice for random errors using A* along with a variety of pruning heuristics. We show through benchmark circuits for surface, color, and bivariate-bicycle codes that Tesseract is competitive with integer programming-based decoders at moderate physical error rates. Finally, we compare surface and bivariate bicycle codes using most-likely error decoding
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Tesseract: A Search-Based Decoder for Quantum Error Correction
Laleh Beni
Oscar Higgott
Noah Shutty
2025
Preview abstract
Tesseract is a Most-Likely-Error decoder designed for quantum error-correcting codes. Tesseract conducts a search through an graph on the set of all subsets of errors to find the lowest cost subset of errors consistent with the input syndrome. Although this set is exponentially large, the search can be made efficient in practice for random errors using A* along with a variety of pruning heuristics. We show through benchmark circuits for surface, color, and bivariate-bicycle codes that Tesseract is competitive with integer programming-based decoders at moderate physical error rates. Finally, we compare surface and bivariate bicycle codes using most-likely error decoding
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Junction and inductor models in ADS
arXiv (2025)
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This note is a follow up to Ref. [Naaman, IEEE TAS 2025], describing how to construct Josephson junction, inductor, and mutual inductance models using components that are available in the Keysight ADS core library.
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Quantum learning advantage on a scalable photonic platform
Jens A. H. Nielsen
Changhun Oh
Senrui Chen
Yat Wong
Robert Huang
Zhenghao Liu
Liang Jiang
Oscar Cordero
John Preskill
Axel B. Bregnsbo
Romain Jeremie Baptiste Brunel
Jonas S. Neergaard-Nielsen
Sisi Zhou
Emil E. B. Ostergaard
Ulrik L. Andersen
Science (2025)
Preview abstract
Recent advancements in quantum technologies have opened new horizons for exploring the physical world in ways once deemed impossible. Central to these breakthroughs is the concept of quantum advantage, where quantum systems outperform their classical counterparts in solving specific tasks. While much attention has been devoted to computational speedups, quantum advantage in learning physical systems remains a largely untapped frontier. Here, we present a photonic implementation of a quantum-enhanced protocol for learning the probability distribution of a multimode bosonic displacement channel. By harnessing the unique properties of continuous-variable quantum entanglement, we achieve high-precision reconstruction of the displacement distribution using multiple orders of magnitude fewer experiments compared to methods that do not employ entangled resources. Specifically, with approximately $5$ dB of two-mode squeezing---corresponding to imperfect Einstein--Podolsky--Rosen (EPR) entanglement---we successfully reconstruct a 100-mode bosonic displacement channel, requiring $10^{11}$ fewer experiments than a conventional measurement scheme. Our results demonstrate that even with non-ideal, noisy entanglement, a significant quantum advantage can be realized in continuous-variable quantum systems. This marks an important step towards practical quantum-enhanced learning protocols with implications for quantum metrology, certification and machine learning.
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Analyzing Prospects for Quantum Advantage in Topological Data Analysis
Dominic W. Berry
Yuan Su
Casper Gyurik
Robbie King
Joao Basso
Abhishek Rajput
Nathan Wiebe
Vedran Djunko
PRX Quantum, 5 (2024), pp. 010319
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Lloyd et al. were first to demonstrate the promise of quantum algorithms for computing Betti numbers in persistent homology (a way of characterizing topological features of data sets). Here, we propose, analyze, and optimize an improved quantum algorithm for topological data analysis (TDA) with reduced scaling, including a method for preparing Dicke states based on inequality testing, a more efficient amplitude estimation algorithm using Kaiser windows, and an optimal implementation of eigenvalue projectors based on Chebyshev polynomials. We compile our approach to a fault-tolerant gate set and estimate constant factors in the Toffoli complexity. Our analysis reveals that super-quadratic quantum speedups are only possible for this problem when targeting a multiplicative error approximation and the Betti number grows asymptotically. Further, we propose a dequantization of the quantum TDA algorithm that shows that having exponentially large dimension and Betti number are necessary, but insufficient conditions, for super-polynomial advantage. We then introduce and analyze specific problem examples for which super-polynomial advantages may be achieved, and argue that quantum circuits with tens of billions of Toffoli gates can solve some seemingly classically intractable instances.
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Drug Design on Quantum Computers
Raffaele Santagati
Alán Aspuru-Guzik
Matthias Degroote
Leticia Gonzalez
Elica Kyoseva
Nikolaj Moll
Markus Oppel
Robert Parrish
Michael Streif
Christofer Tautermann
Horst Weiss
Nathan Wiebe
Clemens Utschig-Utschig
Nature Physics (2024)
Preview abstract
The promised industrial applications of quantum computers often rest on their anticipated ability to perform accurate, efficient quantum chemical calculations. Computational drug discovery relies on accurate predictions of how candidate drugs interact with their targets in a cellular environment involving several thousands of atoms at finite temperatures. Although quantum computers are still far from being used as daily tools in the pharmaceutical industry, here we explore the challenges and opportunities of applying quantum computers to drug design. We discuss where these could transform industrial research and identify the substantial further developments needed to reach this goal.
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Quantum Computation of Stopping power for Inertial Fusion Target Design
Dominic Berry
Alina Kononov
Alec White
Joonho Lee
Andrew Baczewski
Proceedings of the National Academy of Sciences, 121 (2024), e2317772121
Preview abstract
Stopping power is the rate at which a material absorbs the kinetic energy of a charged particle passing through it - one of many properties needed over a wide range of thermodynamic conditions in modeling inertial fusion implosions. First-principles stopping calculations are classically challenging because they involve the dynamics of large electronic systems far from equilibrium, with accuracies that are particularly difficult to constrain and assess in the warm-dense conditions preceding ignition. Here, we describe a protocol for using a fault-tolerant quantum computer to calculate stopping power from a first-quantized representation of the electrons and projectile. Our approach builds upon the electronic structure block encodings of Su et al. [PRX Quantum 2, 040332 2021], adapting and optimizing those algorithms to estimate observables of interest from the non-Born-Oppenheimer dynamics of multiple particle species at finite temperature. We also work out the constant factors associated with a novel implementation of a high order Trotter approach to simulating a grid representation of these systems. Ultimately, we report logical qubit requirements and leading-order Toffoli costs for computing the stopping power of various projectile/target combinations relevant to interpreting and designing inertial fusion experiments. We estimate that scientifically interesting and classically intractable stopping power calculations can be quantum simulated with
roughly the same number of logical qubits and about one hundred times more Toffoli gates than is required for state-of-the-art quantum simulations of industrially relevant molecules such as FeMoCo or P450.
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