When applied on some particular quantum entangled states, measurements are universal for quantum computing. In particular, despite the fondamental probabilistic evolution of quantum measurements, any unitary evolution can be simulated by a measurement-based quantum computer (MBQC). We consider the extended version of the MBQC where each measurement can occur not only in the (X,Y)-plane of the Bloch sphere but also in the (X,Z)- and (Y,Z)-planes. The existence of a gflow in the underlying graph of the computation is a necessary and sufficient condition for a certain kind of determinism. We extend the focused gflow (a gflow in a particular normal form) defined for the (X,Y)-plane to the extended case, and we provide necessary and sufficient conditions for the existence of such normal forms.
In spin systems, the decay of the Loschmidt echo in the time-reversal experiment (evolution, perturbation, time-reversed evolution) is linked to the generation of multiple-quantum coherences. The approach is extended to other systems, and the general problem of reversibility of quantum dynamics is analyzed.
We study the power of dephasing-covariant operations in the resource theories of coherence and entanglement. These are quantum operations whose actions commute with a projective measurement. In the resource theory of coherence, we find that any two states are asymptotically interconvertible under dephasing-covariant operations. This provides a rare example of a resource theory in which asymptotic reversibility can be attained without needing the maximal set of resource non-generating operations. When extended to the resource theory of entanglement, the resultant operations share similarities w…
The principle of microscopic reversibility lies at the core of fluctuation theorems, which have extended our understanding of the second law of thermodynamics to the statistical level. In the quantum regime, however, this elementary principle should be amended as the system energy cannot be sharply determined at a given quantum phase space point. In this Letter, we propose and experimentally test a quantum generalization of the microscopic reversibility when a quantum system interacts with a heat bath through energy-preserving unitary dynamics. Quantum effects can be identified by noting that …
We argue that if, in order to reverse an object's dynamics, we need to be able to keep track of it with enough precision, then there is an upper bound on the size of the object whose dynamics we can reverse - even using all the available resources of the universe. Using a bound from the holographic principle and treating the universe as the ultimate quantum computer, we show that if we want to reverse the dynamics of an object which has evolved since the beginning of time, its radius cannot exceed ten microns. If this computation is performed irreversibly, the object must be much smaller. This…
Quantum measurement is a basic tool to manifest intrinsic quantum effects from fundamental tests to quantum information applications. While a measurement is typically performed to gain information on a quantum state, its role in quantum technology is indeed manifold. For instance, quantum measurement is a crucial process element in measurement-based quantum computation. It is also used to detect and correct errors thereby protecting quantum information in error-correcting frameworks. It is therefore important to fully characterize the roles of quantum measurement encompassing information gain,…
Several kinds of quantum pushdown automaton models have been proposed, and their computational power is investigated intensively. However, for some quantum pushdown automaton models, it is not known whether quantum models are at least as powerful as classical counterparts or not. This is due to the reversibility restriction. In this paper, we introduce a new quantum pushdown automaton model that has a garbage tape. This model can overcome the reversibility restriction by exploiting the garbage tape to store popped symbols. We show that the proposed model can simulate any quantum pushdown autom…
Discovering state-of-the-art quantum circuits with large language models
Harvard Quantum Initiative for Science and Engineering（哈佛量子科学与工程倡议）；Department of Physics, Harvard University（哈佛大学物理系）；Anthropic；QuEra Computing（QuEra计算公司）
The relation between entropy and information has great significance for computation. Based on the strict reversibility of the laws of microphysics, Landauer (1961), Bennett (1973), Priese (1976), Fredkin and Toffoli (1982), Feynman (1985) and others envisioned a reversible computer that cannot allow any ambiguity in backward steps of a calculation. It is this backward capacity that makes reversible computing radically different from ordinary, irreversible computing. The proposal aims at a higher kind of computer that would give the actual output of a computation together with the original inpu…
This paper focuses on the study of topological features in teleportation-based quantum computation as well as aims at presenting a detailed review on teleportaiton-based quantum computation (Gottesman and Chuang, Nature 402, 390, 1999). In the extended Temperley-Lieb diagrammatical approach, we clearly show that such topological features bring about the fault-tolerant construction of both universal quantum gates and four-partite entangled states more intuitive and simpler. Furthermore, we describe the Yang--Baxter gate by its extended Temperley-Lieb configuration, and then study teleportation-…
Graph states are an elegant and powerful quantum resource for measurement based quantum computation (MBQC). They are also used for many quantum protocols (error correction, secret sharing, etc.). The main focus of this paper is to provide a structural characterisation of the graph states that can be used for quantum information processing. The existence of a gflow (generalized flow) is known to be a requirement for open graphs (graph, input set and output set) to perform uniformly and strongly deterministic computations. We weaken the gflow conditions to define two new more general kinds of MB…
The efficient certification of classically intractable quantum devices has been a central research question for some time. However, to observe a "quantum advantage", it is believed that one does not need to build a large scale universal quantum computer, a task which has proven extremely challenging. Intermediate quantum models that are easier to implement, but which also exhibit this quantum advantage over classical computers, have been proposed. In this work, we present a certification technique for such a sub-universal quantum server which only performs commuting gates and requires very lim…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by having it follow from two main postulates (i) the theory should be logically consistent; (ii) inferences in the theory should be computable in polynomial time. The first postulate is what we require to each well-founded mathematical theory. The computation postulate defines the physical component of the theory. We show that the computation postulate is the only true divide betwee…
Clifford gates are a winsome class of quantum operations combining mathematical elegance with physical significance. The Gottesman-Knill theorem asserts that Clifford computations can be classically efficiently simulated but this is true only in a suitably restricted setting. Here we consider Clifford computations with a variety of additional ingredients: (a) strong vs. weak simulation, (b) inputs being computational basis states vs. general product states, (c) adaptive vs. non-adaptive choices of gates for circuits involving intermediate measurements, (d) single line outputs vs. multi-line ou…
This paper presents an equational theory for the QRAM model of quantum computation, formulated as an embedded language inside of homotopy type theory. The embedded language approach is highly expressive, and reflects the style of state-of-the art quantum languages like Quipper and QWIRE. The embedding takes advantage of features of homotopy type theory to encode unitary transformations as higher inductive paths, simplifying the presentation of an equational theory. We prove that this equational theory is sound and complete with respect to established models of quantum computation.
