arXiv subjects

Michael J. Bremner

Publications and source records attributed to Michael J. Bremner.

At least 19 recordsLinked to original sources

arXiv2026

Prospects for Quantum Computation in Propellant Design: Assessing the Stability of Cyclic Ozone in Nanoscale Confinement

Cyclic ozone additives have the potential to markedly increase the specific impulse of rocket fuel. This would translate to greater efficiency and reduced costs for space lift by granting more payload per rocket. While practical efforts to capture this isomer have been unsuccessful, it is possible that cyclic ozone would be stabilized in confined geometries. The required synthetic methods are nonetheless difficult to design and require theory-driven inputs that lie beyond the scope of classical methods. Quantum computation has the potential to enable these calculations, though the underlying hardware requirements remain unclear for many practical applications. We present an end-to-end analysis of how quantum methods could support efforts to isolate cyclic ozone via fullerene encapsulation. Our discussion extends beyond asymptotic complexity, reporting both logical- and physical-level resource estimates for ground-state energy determination via quantum phase estimation (QPE), computed using multiple independent resource estimation stacks - Azure Quantum Resource Estimator (AzureQRE), PennyLane's resource estimation framework, and MIT Lincoln Lab's pyLIQTR toolkit - to cross-check resource estimates and bracket realistic overheads. Taken collectively, these data delineate a plausible scale for realistic, computationally-aided molecular design efforts using fault-tolerant quantum computation.

quant-ph↗

arXiv2026

Dissipative continuation for ground-state preparation at chemical transition states

Simulating chemical reactions exhibits a pronounced unevenness in computational difficulty: while equilibrium reactant and product geometries are often tractable, transition-state (TS) geometries frequently display strong multi-reference character that challenges both classical solvers and coherent quantum state-preparation methods. We introduce a dissipative continuation protocol for preparing electronic ground states near TS geometries within a hybrid classical--quantum workflow. In the intended setting, classical electronic-structure methods supply an approximate TS geometry, a computationally motivated continuation path, and a locally compatible active-space representation along that path. Starting from a warm start at a tractable geometry on the same aligned path, the quantum routine transports the state toward the TS using orbital-gauge-aligned Hamiltonians and engineered dissipative cooling primitives that repeatedly contract population into the instantaneous low-energy sector. We prove that, for continuation paths satisfying a Lipschitz smoothness condition and a localized Eigenstate Thermalization Hypothesis (ETH)-motivated downward-drift condition within the relevant energy window, the ground state at the target geometry can be prepared to total energy error $ε_E$ with total ideal cooling-step complexity $\widetilde{O}(C_{\mathrm{DK}}^2 N_o^2 / ε_E)$. Here $C_{\mathrm{DK}}$ quantifies ground-state rotation along the aligned path. The corresponding logical gate count is obtained by multiplying this primitive count by the cost of implementing one dissipative step, which is polynomial in the block-encoding size of the Lindbladian under standard Lindblad-simulation algorithms. This identifies a structured regime in which dissipative continuation provides a conditional route to ground-state preparation at strongly correlated TS geometries.

quant-ph↗

arXiv2026

The Complexity of Local Stoquastic Hamiltonians on 2D Lattices

We show the 2-Local Stoquastic Hamiltonian problem on a 2D square qubit lattice is StoqMA-complete. We achieve this by extending the spatially sparse circuit construction of Oliveira and Terhal, as well as the perturbative gadgets of Bravyi, DiVincenzo, Oliveira, and Terhal. Our main contributions demonstrate StoqMA circuits can be made spatially sparse and that geometrical, stoquastic-preserving, perturbative gadgets can be constructed, without an increase to particle dimension.

quant-ph↗

arXiv2025

Quantum computing for corrosion-resistant materials and anti-corrosive coatings design

Corrosion is a pervasive issue that impacts the structural integrity and performance of materials across various industries, imposing a significant economic impact globally. In fields like aerospace and defense, developing corrosion-resistant materials is critical, but progress is often hindered by the complexities of material-environment interactions. While computational methods have advanced in designing corrosion inhibitors and corrosion-resistant materials, they fall short in understanding the fundamental corrosion mechanisms due to the highly correlated nature of the systems involved. This paper explores the potential of leveraging quantum computing to accelerate the design of corrosion inhibitors and corrosion-resistant materials, with a particular focus on magnesium and niobium alloys. We investigate the quantum computing resources required for high-fidelity electronic ground-state energy estimation (GSEE), which will be used in our hybrid classical-quantum workflow. Representative computational models for magnesium and niobium alloys show that 2292 to 38598 logical qubits and $(1.04$ to $1962) \times 10^{13}$ T-gates are required for simulating the ground-state energy of these systems under the first quantization encoding using plane waves basis.

quant-ph↗

arXiv2024

Instantaneous Quantum Polynomial-Time Sampling and Verifiable Quantum Advantage: Stabilizer Scheme and Classical Security

Sampling problems demonstrating beyond classical computing power with noisy intermediate scale quantum devices have been experimentally realized. In those realizations, however, our trust that the quantum devices faithfully solve the claimed sampling problems is usually limited to simulations of smaller-scale instances and is, therefore, indirect. The problem of verifiable quantum advantage aims to resolve this critical issue and provides us with greater confidence in a claimed advantage. Instantaneous quantum polynomial-time (IQP) sampling has been proposed to achieve beyond classical capabilities with a verifiable scheme based on quadratic-residue codes (QRC). Unfortunately, this verification scheme was recently broken by an attack proposed by Kahanamoku-Meyer. In this work, we revive IQP-based verifiable quantum advantage by making two major contributions. Firstly, we introduce a family of IQP sampling protocols called the stabilizer scheme, which builds on results linking IQP circuits, the stabilizer formalism, coding theory, and an efficient characterization of IQP circuit correlation functions. This construction extends the scope of existing IQP-based schemes while maintaining their simplicity and verifiability. Secondly, we introduce the Hidden Structured Code (HSC) problem as a well-defined mathematical challenge that underlies the stabilizer scheme. To assess classical security, we explore a class of attacks based on secret extraction, including the Kahanamoku-Meyer's attack as a special case. We provide evidence of the security of the stabilizer scheme, assuming the hardness of the HSC problem. We also point out that the vulnerability observed in the original QRC scheme is primarily attributed to inappropriate parameter choices, which can be naturally rectified with proper parameter settings.

quant-ph↗

arXiv2023

Transversal Injection: Using the Surface Code to Prepare Non-Pauli Eigenstates

The development of quantum computing systems for large scale algorithms requires targeted error rates unachievable through hardware advancements alone. Quantum Error Correction (QEC) allows us to use systems with a large number of physical qubits to form a fault tolerant system with a lower number of logical qubits and a favourable logical error rate. While some gates can be easily implemented in a QEC code transversally, there is no code that has a universal set of transversal gates. Transversal Injection is a new method of preparing logical non-Pauli eigenstates that can be used as resource states for quantum computation. State preparation can be done directly in the surface code and has the potential to prepare higher fidelity injected states. Compared to other techniques, transversal injection can reduce the resource burden for state distillation protocols. In this paper, the authors present the theory behind this new technique as well as an algorithm for calculating the resulting logical states prepared in the surface code.

quant-ph↗

arXiv2022

Quantum computation on a 19-qubit wide 2d nearest neighbour qubit array

In this paper, we explore the relationship between the width of a qubit lattice constrained in one dimension and physical thresholds for scalable, fault-tolerant quantum computation. To circumvent the traditionally low thresholds of small fixed-width arrays, we deliberately engineer an error bias at the lowest level of encoding using the surface code. We then address this engineered bias at a higher level of encoding using a lattice-surgery surface code bus that exploits this bias, or a repetition code to make logical qubits with unbiased errors out of biased surface code qubits. Arbitrarily low error rates can then be reached by further concatenating with other codes, such as Steane [[7,1,3]] code and the [[15,7,3]] CSS code. This enables a scalable fixed-width quantum computing architecture on a square qubit lattice that is only 19 qubits wide, given physical qubits with an error rate of $8.0\times 10^{-4}$. This potentially eases engineering issues in systems with fine qubit pitches, such as quantum dots in silicon or gallium arsenide.

quant-ph↗

arXiv2022

Transversal Injection: A method for direct encoding of ancilla states for non-Clifford gates using stabiliser codes

Fault-tolerant, error-corrected quantum computation is commonly acknowledged to be crucial to the realisation of large-scale quantum algorithms that could lead to extremely impactful scientific or commercial results. Achieving a universal set of quantum gate operations in a fault-tolerant error-corrected framework suffers from a `conservation of unpleasantness'. In general, no matter what error correction technique is employed, there is always one element of a universal gate set that carries a significant resource overhead - either in physical qubits, computational time, or both. Specifically, this is due to the application of non-Clifford gates. A common method for realising these gates for stabiliser codes such as the surface code is a combination of three protocols: state injection, distillation and gate teleportation. These protocols contribute to the resource overhead compared to logical operations such as a CNOT gate and contributes to the qubit resources for any error-corrected quantum algorithm. In this paper, we introduce a very simple protocol to potentially reduce this overhead for non-Clifford gates: Transversal Injection. Transversal injection modifies the initial physical states of all data qubits in a stabiliser code before standard encoding and results in the direct preparation of a large class of single qubit states, including resource states for non-Clifford logic gates. Preliminary results hint at high quality fidelities at larger distances and motivate further research on this technique.

quant-ph↗

arXiv2022

Parameterized Complexity of Weighted Local Hamiltonian Problems and the Quantum Exponential Time Hypothesis

We study a parameterized version of the local Hamiltonian problem, called the weighted local Hamiltonian problem, where the relevant quantum states are superpositions of computational basis states of Hamming weight $k$. The Hamming weight constraint can have a physical interpretation as a constraint on the number of excitations allowed or particle number in a system. We prove that this problem is in QW[1], the first level of the quantum weft hierarchy and that it is hard for QM[1], the quantum analogue of M[1]. Our results show that this problem cannot be fixed-parameter quantum tractable (FPQT) unless certain natural quantum analogue of the exponential time hypothesis (ETH) is false.

cs.CC↗

arXiv2022

Quantum Parameterized Complexity

Parameterized complexity theory was developed in the 1990s to enrich the complexity-theoretic analysis of problems that depend on a range of parameters. In this paper we establish a quantum equivalent of classical parameterized complexity theory, motivated by the need for new tools for the classifications of the complexity of real-world problems. We introduce the quantum analogues of a range of parameterized complexity classes and examine the relationship between these classes, their classical counterparts, and well-studied problems. This framework exposes a rich classification of the complexity of parameterized versions of QMA-hard problems, demonstrating, for example, a clear separation between the Quantum Circuit Satisfiability problem and the Local Hamiltonian problem.

quant-ph↗

arXiv2019

Approximation Algorithms for Complex-Valued Ising Models on Bounded Degree Graphs

We study the problem of approximating the Ising model partition function with complex parameters on bounded degree graphs. We establish a deterministic polynomial-time approximation scheme for the partition function when the interactions and external fields are absolutely bounded close to zero. Furthermore, we prove that for this class of Ising models the partition function does not vanish. Our algorithm is based on an approach due to Barvinok for approximating evaluations of a polynomial based on the location of the complex zeros and a technique due to Patel and Regts for efficiently computing the leading coefficients of graph polynomials on bounded degree graphs. Finally, we show how our algorithm can be extended to approximate certain output probability amplitudes of quantum circuits.

quant-ph↗

arXiv2017

On the Complexity of Random Quantum Computations and the Jones Polynomial

There is a natural relationship between Jones polynomials and quantum computation. We use this relationship to show that the complexity of evaluating relative-error approximations of Jones polynomials can be used to bound the classical complexity of approximately simulating random quantum computations. We prove that random quantum computations cannot be classically simulated up to a constant total variation distance, under the assumption that (1) the Polynomial Hierarchy does not collapse and (2) the average-case complexity of relative-error approximations of the Jones polynomial matches the worst-case complexity over a constant fraction of random links. Our results provide a straightforward relationship between the approximation of Jones polynomials and the complexity of random quantum computations.

quant-ph↗

arXiv2017

Achieving quantum supremacy with sparse and noisy commuting quantum computations

The class of commuting quantum circuits known as IQP (instantaneous quantum polynomial-time) has been shown to be hard to simulate classically, assuming certain complexity-theoretic conjectures. Here we study the power of IQP circuits in the presence of physically motivated constraints. First, we show that there is a family of sparse IQP circuits that can be implemented on a square lattice of n qubits in depth O(sqrt(n) log n), and which is likely hard to simulate classically. Next, we show that, if an arbitrarily small constant amount of noise is applied to each qubit at the end of any IQP circuit whose output probability distribution is sufficiently anticoncentrated, there is a polynomial-time classical algorithm that simulates sampling from the resulting distribution, up to constant accuracy in total variation distance. However, we show that purely classical error-correction techniques can be used to design IQP circuits which remain hard to simulate classically, even in the presence of arbitrary amounts of noise of this form. These results demonstrate the challenges faced by experiments designed to demonstrate quantum supremacy over classical computation, and how these challenges can be overcome.

quant-ph↗

arXiv2017

Characterizing Quantum Supremacy in Near-Term Devices

A critical question for the field of quantum computing in the near future is whether quantum devices without error correction can perform a well-defined computational task beyond the capabilities of state-of-the-art classical computers, achieving so-called quantum supremacy. We study the task of sampling from the output distributions of (pseudo-)random quantum circuits, a natural task for benchmarking quantum computers. Crucially, sampling this distribution classically requires a direct numerical simulation of the circuit, with computational cost exponential in the number of qubits. This requirement is typical of chaotic systems. We extend previous results in computational complexity to argue more formally that this sampling task must take exponential time in a classical computer. We study the convergence to the chaotic regime using extensive supercomputer simulations, modeling circuits with up to 42 qubits - the largest quantum circuits simulated to date for a computational task that approaches quantum supremacy. We argue that while chaotic states are extremely sensitive to errors, quantum supremacy can be achieved in the near-term with approximately fifty superconducting qubits. We introduce cross entropy as a useful benchmark of quantum circuits which approximates the circuit fidelity. We show that the cross entropy can be efficiently measured when circuit simulations are available. Beyond the classically tractable regime, the cross entropy can be extrapolated and compared with theoretical estimates of circuit fidelity to define a practical quantum supremacy test.

quant-ph↗

arXiv2017

Quantum Sampling Problems, BosonSampling and Quantum Supremacy

There is a large body of evidence for the potential of greater computational power using information carriers that are quantum mechanical over those governed by the laws of classical mechanics. But the question of the exact nature of the power contributed by quantum mechanics remains only partially answered. Furthermore, there exists doubt over the practicality of achieving a large enough quantum computation that definitively demonstrates quantum supremacy. Recently the study of computational problems that produce samples from probability distributions has added to both our understanding of the power of quantum algorithms and lowered the requirements for demonstration of fast quantum algorithms. The proposed quantum sampling problems do not require a quantum computer capable of universal operations and also permit physically realistic errors in their operation. This is an encouraging step towards an experimental demonstration of quantum algorithmic supremacy. In this paper, we will review sampling problems and the arguments that have been used to deduce when sampling problems are hard for classical computers to simulate. Two classes of quantum sampling problems that demonstrate the supremacy of quantum algorithms are BosonSampling and IQP Sampling. We will present the details of these classes and recent experimental progress towards demonstrating quantum supremacy in BosonSampling.

quant-ph↗

arXiv2015

Average-case complexity versus approximate simulation of commuting quantum computations

We use the class of commuting quantum computations known as IQP (Instantaneous Quantum Polynomial time) to strengthen the conjecture that quantum computers are hard to simulate classically. We show that, if either of two plausible average-case hardness conjectures holds, then IQP computations are hard to simulate classically up to constant additive error. One conjecture relates to the hardness of estimating the complex-temperature partition function for random instances of the Ising model; the other concerns approximating the number of zeroes of random low-degree polynomials. We observe that both conjectures can be shown to be valid in the setting of worst-case complexity. We arrive at these conjectures by deriving spin-based generalisations of the Boson Sampling problem that avoid the so-called permanent anticoncentration conjecture.

quant-ph↗

arXiv2010

Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy

We consider quantum computations comprising only commuting gates, known as IQP computations, and provide compelling evidence that the task of sampling their output probability distributions is unlikely to be achievable by any efficient classical means. More specifically we introduce the class post-IQP of languages decided with bounded error by uniform families of IQP circuits with post-selection, and prove first that post-IQP equals the classical class PP. Using this result we show that if the output distributions of uniform IQP circuit families could be classically efficiently sampled, even up to 41% multiplicative error in the probabilities, then the infinite tower of classical complexity classes known as the polynomial hierarchy, would collapse to its third level. We mention some further results on the classical simulation properties of IQP circuit families, in particular showing that if the output distribution results from measurements on only O(log n) lines then it may in fact be classically efficiently sampled.

quant-ph↗

arXiv2009

Instantaneous Quantum Computation

We examine theoretic architectures and an abstract model for a restricted class of quantum computation, called here instantaneous quantum computation because it allows for essentially no temporal structure within the quantum dynamics. Using the theory of binary matroids, we argue that the paradigm is rich enough to enable sampling from probability distributions that cannot, classically, be sampled from efficiently and accurately. This paradigm also admits simple interactive proof games that may convince a skeptic of the existence of truly quantum effects. Furthermore, these effects can be created using significantly fewer qubits than are required for running Shor's Algorithm.

quant-ph↗