arXiv subjects

Isaac D. Smith

Publications and source records attributed to Isaac D. Smith.

8 recordsLinked to original sources

arXiv2026

Necessary and Sufficient Conditions for Universal Gates with Pauli Strings and Beyond

Any quantum computation consists of a sequence of unitary evolutions described by a finite set of Hamiltonians. For the case where this set consists of only products of Pauli operators, known as Pauli strings, we provide a necessary and sufficient condition for it to generate $\mathfrak{su}(2^n)$, i.e., to be universal for quantum computation on $n$ qubits. When combining Pauli strings with a general Hamiltonian, we show a sufficient (and in certain circumstances even necessary) condition for universality based on the Pauli-basis expansion of the Hamiltonian. As an application of these results, we prove two corollaries: (i) a necessary and sufficient condition for the universality of a general Hamiltonian given arbitrary single-qubit control on all qubits, and (ii) the universality of an XYZ Heisenberg Hamiltonian with local control of just two adjacent qubits.

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arXiv2025

Efficient Preparation of Resource States for Hamiltonian Simulation and Universal Quantum Computation

The direct compilation of algorithm-specific graph states in measurement-based quantum computation (MBQC) can lead to resource reductions in terms of circuit depth, entangling gates, and even the number of physical qubits. In this work, we extend previous studies on algorithm-tailored graph states to periodic sequences of generalized Pauli rotations, which commonly appear in, e.g., Trotterized Hamiltonian simulation. We first implement an enhanced simulated-annealing-based algorithm to find optimal periodic graph states within local-Clifford equivalent MBQC resources. In addition, we derive a novel scheme for the preparation of resource states based on a graph state and a ladder of CNOT gates, which we term anticommutation-based MBQC, since it uncovers a direct relationship between the graph state and the anticommutation matrix for the set of Hamiltonians generating the computation. We also deploy our two approaches to derive universal resource states from minimal universal sets of generating Hamiltonians. Finally, we demonstrate and compare both of our methods based on various examples from condensed matter physics and universal quantum computation.

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arXiv2025

Minimally Universal Parity Quantum Computing

In parity quantum computing, multi-qubit logical gates are implemented by single-qubit rotations on a suitably encoded state involving auxiliary qubits. Consequently, there is a correspondence between qubit count and the size of the native gate set. One might then wonder: what is the smallest number of auxiliary qubits that still allows for universal parity computing? Here, we demonstrate that the answer is one, if the number of logical qubits is even, and two otherwise. Furthermore, we present a sufficient condition for a given parity gate set to be universal. This leads to a variety of different universal parity gate sets corresponding to different numbers of auxiliary qubits, and more generally contributes to the understanding of which entangling gates are required to augment the set of single-qubit unitaries to perform universal quantum computing. As a consequence, we obtain (i) minimal implementations of the parity framework on e.g., a triangular lattice, (ii) hardware specific implementations of the parity flow framework on e.g., a heavy-hex lattice, and (iii) novel universal resources for measurement-based quantum computation (MBQC).

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arXiv2025

Optimally generating $\mathfrak{su}(2^N)$ using Pauli strings

Any quantum computation consists of a sequence of unitary evolutions described by a finite set of Hamiltonians. When this set is taken to consist of only products of Pauli operators, we show that the minimal such set generating $\mathfrak{su}(2^{N})$ contains $2N+1$ elements. We provide a number of examples of such generating sets and furthermore provide an algorithm for producing a sequence of rotations corresponding to any given Pauli rotation, which is shown to have optimal complexity. We also observe that certain sets generate $\mathfrak{su}(2^{N})$ at a faster rate than others, and we show how this rate can be optimized by tuning the fraction of anticommuting pairs of generators. Finally, we briefly comment on implications for measurement-based and trapped ion quantum computation as well as the construction of fault-tolerant gate sets.

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arXiv2025

The Work Capacity of Channels with Memory: Maximum Extractable Work in Percept-Action Loops

Predicting future observations plays a central role in machine learning, biology, economics, and many other fields. It lies at the heart of organizational principles such as the variational free energy principle and has even been shown -- based on the second law of thermodynamics -- to be necessary for reaching the fundamental energetic limits of sequential information processing. While the usefulness of the predictive paradigm is undisputed, complex adaptive systems that interact with their environment are more than just predictive machines: they have the power to act upon their environment and cause change. In this work, we develop a framework to analyze the thermodynamics of information processing in percept-action loops -- a model of agent-environment interaction -- allowing us to investigate the thermodynamic implications of actions and percepts on equal footing. To this end, we introduce the concept of work capacity -- the maximum rate at which an agent can expect to extract work from its environment. Our results reveal that neither of two previously established design principles for work-efficient agents -- maximizing predictive power and forgetting past actions -- remains optimal in environments where actions have observable consequences. Instead, a trade-off emerges: work-efficient agents must balance prediction and forgetting, as remembering past actions can reduce the available free energy. This highlights a fundamental departure from the thermodynamics of passive observation, suggesting that prediction and energy efficiency may be at odds in active learning systems.

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arXiv2025

Parity Quantum Computing as YZ-Plane Measurement-Based Quantum Computing

We show that universal parity quantum computing employing a recently introduced constant depth decoding procedure is equivalent to measurement-based quantum computation (MBQC) on a bipartite graph using only YZ-plane measurements. We further show that any unitary MBQC using only YZ-plane measurements must occur on a bipartite graph.

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arXiv2025

Fully quantum inflation: quantum marginal problem constraints in the service of causal inference

Consider the problem of deciding, for a particular multipartite quantum state, whether or not it is realizable in a quantum network with a particular causal structure. This is a fully quantum version of what causal inference researchers refer to as the problem of causal discovery. In this work, we introduce a fully quantum version of the inflation technique for causal inference, which leverages the quantum marginal problem. The primary example by which we illustrate the utility of this method is testing compatibility of tripartite quantum states with the quantum network known as the triangle scenario. We show, in particular, how the method yields a complete classification of pure three-qubit states into those that are and those that are not compatible with the triangle scenario. We also provide some illustrative examples involving mixed states and some where one or more of the systems is higher-dimensional. Furthermore, we examine the question of when the incompatibility of a multipartite quantum state with a causal structure can be inferred from the incompatibility of a joint probability distribution induced by implementing measurements on each subsystem. Finally, we present a family of networks, which include the triangle scenario as a special case, for which causal compatibility constraints can be derived.

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arXiv2023

The Min-Entropy of Classical-Quantum Combs for Measurement-Based Applications

Learning a hidden property of a quantum system typically requires a series of interactions. In this work, we formalise such multi-round learning processes using a generalisation of classical-quantum states, called classical-quantum combs. Here, "classical" refers to a random variable encoding the hidden property to be learnt, and "quantum" refers to the quantum comb describing the behaviour of the system. The optimal strategy for learning the hidden property can be quantified by applying the comb min-entropy (Chiribella and Ebler, NJP, 2016) to classical-quantum combs. To demonstrate the power of this approach, we focus attention on an array of problems derived from measurement-based quantum computation (MBQC) and related applications. Specifically, we describe a known blind quantum computation (BQC) protocol using the combs formalism and thereby leverage the min-entropy to provide a proof of single-shot security for multiple rounds of the protocol, extending the existing result in the literature. Furthermore, we consider a range of operationally motivated examples related to the verification of a partially unknown MBQC device. These examples involve learning the features of the device necessary for its correct use, including learning its internal reference frame for measurement calibration. We also introduce a novel connection between MBQC and quantum causal models that arises in this context.

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