arXiv subjects

Mischa P. Woods

Publications and source records attributed to Mischa P. Woods.

At least 19 recordsLinked to original sources

arXiv2026

A Square-Root Barrier to Quantum Gate Speed under Linear Coupling

Faster quantum gates can suppress the decoherence accumulated during a computation, but in superconducting processors stronger microwave pulses can also increase leakage, off-resonant excitation, stray-field errors, and crosstalk. This creates a central energy--speed--error tradeoff: can quantum state engineering make a gate parametrically faster without paying proportionally more drive energy? We address this question by treating the driving pulse as a quantum bosonic field rather than a classical waveform. For a finite-dimensional system coupled linearly to that field, we prove that fixed-fidelity gate transition rates grow at most as the square root of the pulse energy, under stated uniformity conditions on the coupling and accepted dynamics. The bound permits arbitrary pulse states, including squeezed and non-Gaussian states, as well as drive--system entanglement and back action; coherent Gaussian pulses attain its energy exponent. Thus squeezing or other state engineering alone cannot replace the square-root energy law of a conventional linear drive by the linear scaling allowed by general quantum speed limits. Achieving that improvement requires changing the interaction class, in addition to using a suitable nonclassical pulse, thereby identifying interaction nonlinearity as an essential resource for relaxing the practical gate-speed error tradeoff.

quant-ph↗

arXiv2026

Quantum theory based on real numbers cannot be experimentally falsified

Whether the complex numbers of standard quantum theory are experimentally indispensable has remained open for decades. Real quantum theory (RQT), obtained by replacing complex amplitudes with real ones while retaining the usual Kronecker-product composition rule, reproduces all single-party and bipartite Bell correlations of quantum theory (QT), but its lack of local tomography suggested that the two theories might diverge in more general local experiments. This possibility appeared to be confirmed by Renou et al., who argued that a bilocal network experiment can falsify RQT without falsifying QT. Here we show that this conclusion relies on an experimentally untestable assumption. The key distinction is between product-state independence, which constrains the mathematical form of source states, and operational independence, which is defined entirely by the absence of observable cross-source correlations. We prove that, once source independence is imposed operationally, every finite network correlation achievable in QT is also achievable in RQT with the same locality structure of the measurements. We then extend this equivalence to arbitrary finite sequential multipartite protocols involving channels and measurements with prescribed locality structure. Thus, as long as no violation of QT is observed, RQT cannot be experimentally falsified. Our results restore the empirical indistinguishability of QT and RQT, while showing that they support markedly different pictures of the correlation structure underlying the same observed world.

quant-ph↗

arXiv2025

Quantum theory does not need complex numbers

Quantum theory was radically different from the theories of nature which came before it. One key difference was its use of complex numbers. This opened a longstanding debate over whether quantum theory fundamentally requires complex numbers -- or if their use is merely a convenient choice. Until recently, this question was considered open. However, in a 2021 Nature article, a decisive argument was presented asserting that quantum theory needs complex numbers since real-number quantum theory is inconsistent with the postulates of quantum theory. In this work, we show that this conclusion was premature, and in actual fact, a real-number quantum theory is consistent with the postulates of quantum theory. Our theory retains key features such as representation locality (i.e. local physical operations are represented by local changes to the states). A direct consequence of our results is that quantum theory based on real or complex numbers are experimentally indistinguishable.

quant-ph↗

arXiv2025

Quantum Frequential Computing: a quadratic runtime advantage for all computations

An enduring challenge in computer science is reducing the runtime required to solve computational problems. Quantum computing has attracted significant attention due to its potential to deliver asymptotically faster solutions to certain problems compared to the best-known classical algorithms. This advantage is enabled by the quantum mechanical nature of the logical degrees of freedom. To date, it was unknown if permitting other parts of the computer to be quantum mechanical, rather than semi-classical, could yield additional runtime speed-ups as a function of resource utilization (e.g., power consumption or cooling requirements). In this work, we prove that when the control mechanisms associated with gate implementation are optimal quantum mechanical states, a quadratic runtime speedup (with respect to power consumption) is achievable for any algorithm, relative to optimal classical or semi-classical control schemes. Moreover, we demonstrate that only a small fraction of the computer's architecture needs to employ optimal quantum control states to realize this advantage, thereby significantly simplifying the design of future systems. We call this new device a quantum frequential computer, since the quantum speedup arises from an increase in gate frequency. In current state-of-the-art designs, gate frequency is often limited by the coupling strength between components. Notably, our approach achieves the speedup without requiring an increase in coupling strength.

quant-ph↗

arXiv2024

A general quantum circuit framework for Extended Wigner's Friend Scenarios: logically and causally consistent reasoning without absolute measurement events

Extended Wigner's Friend Scenarios (EWFSs) go beyond the standard usage of quantum theory, where agents are treated classically, and instead model agents as unitary evolving quantum systems. This has been the subject of several no-go results: Frauchiger and Renner (FR) suggested that quantum agents reasoning using quantum theory will arrive at logical paradoxes, while other results highlight challenges for having an objective notion of measurement events and for causal reasoning in EWFSs. This raises the question: Is it possible to reliably make and test scientific predictions, and consistently reason about the world when applying quantum theory universally without assuming that observed measurement outcomes are absolute? We give a positive answer by developing a general quantum circuit framework for EWFSs. We formalise the concept of Heisenberg cuts by mapping them to distinct channels in a quantum circuit, and prove that FR-type paradoxes can be fully resolved by making explicit the conditioning on the quantum channels that are used in the reasoning process. We provide concrete rules by which quantum agents can reason and make predictions in a logically and causally consistent manner. Our framework describes all perspectives and predictions of an EWFS within a single, well-defined causal structure, although it allows events to be fundamentally subjective. Moreover, we show that an objective notion of measurement events nevertheless emerges in real-world experiments. This demonstrates the possibility of a relational yet operational framework overcoming challenges to scientific reasoning in EWFSs without modifying the Born rule, quantum unitarity, or the axioms of classical logic and probability theory. This enables analysis of different EWFS arguments and provides a platform to consistently extend quantum information methods and studies to Wigner's Friend Scenarios.

quant-ph↗

arXiv2024

On the feasibility of detecting quantum delocalization effects on relativistic time dilation in optical clocks

We derive the predicted time dilation of delocalized atomic clocks in an optical lattice setup in the presence of a gravitational field to leading order in quantum relativistic corrections. We investigate exotic quantum states of motion whose relativistic time dilation is outside of the realm of classical general relativity, finding a regime where $^{24}\mathrm{Mg}$ optical lattice clocks currently in development would comfortably be able to detect this quantum effect (if the technical challenge of generating such states can be met and the expected accuracy of such clocks can be attained). We provide a detailed experimental protocol and analyse the effects of noise on our predictions. We also show that the magnitude of our predicted quantum relativistic time dilation effect remains just out of detectable reach for the current generation of $^{87}\mathrm{Sr}$ optical lattice clocks. Our calculations agree with the predicted time dilation of classical general relativity when restricting to Gaussian states.

quant-ph↗

arXiv2024

Time-energy uncertainty relation for noisy quantum metrology

Detection of weak forces and precise measurement of time are two of the many applications of quantum metrology to science and technology. We consider a quantum system initialized in a pure state and whose evolution is governed by a Hamiltonian $H$; a measurement can later estimate the time $t$ for which the system has evolved. In this work, we introduce and study a fundamental trade-off which relates the amount by which noise reduces the accuracy of a quantum clock to the amount of information about the energy of the clock that leaks to the environment. Specifically, we consider an idealized scenario in which Alice prepares an initial pure state of the clock, allows the clock to evolve for a time $t$ that is not precisely known, and then transmits the clock through a noisy channel to Bob. The environment (Eve) receives any information that is lost. We prove that Bob's loss of quantum Fisher information (QFI) about $t$ is equal to Eve's gain of QFI about a complementary energy parameter. We also prove a more general trade-off that applies when Bob and Eve wish to estimate the values of parameters associated with two noncommuting observables. We derive the necessary and sufficient conditions for the accuracy of the clock to be unaffected by the noise. These are a subset of the Knill-Laflamme error-correction conditions; states satisfying these conditions are said to form a metrological code. We provide a scheme to construct metrological codes in the stabilizer formalism. We show that there are metrological codes that cannot be written as a quantum error-correcting code with similar distance in which the Hamiltonian acts as a logical operator, potentially offering new schemes for constructing states that do not lose any sensitivity upon application of a noisy channel. We discuss applications of our results to sensing using a many-body state subject to erasure or amplitude-damping noise.

quant-ph↗

arXiv2023

Quantum advantages in timekeeping: dimensional advantage, entropic advantage and how to realise them via Berry phases and ultra-regular spontaneous emission

When an atom is in an excited state, after some amount of time, it will decay to a lower energy state emitting a photon in the process. This is known as spontaneous emission. It is one of the three elementary light-matter interactions. If it has not decayed at time $t$, then the probability that it does so in the next infinitesimal time step $[t, t+δt]$, is $t$-independent. So there is no preferred time at which to decay -- in this sense it is a random process. Here we show, by carefully engineering this light-matter interaction, that we can associate it with a clock, where the matter constitutes the clockwork and the spontaneous emission constitutes the ticking of the clock. In particular, we show how to realise the quasi-ideal clock. Said clock has been proven -- in an abstract and theoretic sense -- to be the most accurate clock permissible by quantum theory, with a polynomial enhancement in precision over the best stochastic clock of the same size. Our results thus demonstrate that the seemingly random process of spontaneous emission can in actual fact, under the right circumstances, be the most regular one permissible by quantum theory. To achieve this we use geometric features and flux-loop insertions to induce symmetry and Berry phases into the light-matter coupling. We also study the entropy the clock produces per tick and show that it also possesses a quantum advantage over that generated from the previously known semi-classical clocks in the literature.

quant-ph↗

arXiv2023

Autonomous Quantum Devices: When Are They Realizable without Additional Thermodynamic Costs?

The resource theory of quantum thermodynamics has been a very successful theory and has generated much follow-up work in the community. It requires energy-preserving unitary operations to be implemented over a system, bath, and catalyst as part of its paradigm. So far, such unitary operations have been considered a "free" resource in the theory. However, this is only an idealization of a necessarily inexact process. Here, we include an additional auxiliary control system which can autonomously implement the unitary by turning an interaction "on or off". However, the control system will inevitably be degraded by the backaction caused by the implementation of the unitary. We derive conditions on the quality of the control device so that the laws of thermodynamics do not change and prove - by utilizing a good quantum clock - that the laws of quantum mechanics allow the backreaction to be small enough so that these conditions are satisfiable. Our inclusion of nonidealized control into the resource framework also raises interesting prospects, which were absent when considering idealized control. Among other things, the emergence of a third law without the need for the assumption of a light cone. Our results and framework unify the field of autonomous thermal machines with the thermodynamic quantum resource-theoretic one, and lay the groundwork for all quantum processing devices to be unified with fully autonomous machines.

quant-ph↗

arXiv2022

On the system loophole of generalized noncontextuality

Generalized noncontextuality is a well-studied notion of classicality that is applicable to a single system, as opposed to Bell locality. It relies on representing operationally indistinguishable procedures identically in an ontological model. However, operational indistinguishability depends on the set of operations that one may use to distinguish two procedures: we refer to this set as the reference of indistinguishability. Thus, whether or not a given experiment is noncontextual depends on the choice of reference. The choices of references appearing in the literature are seldom discussed, but typically relate to a notion of system underlying the experiment. This shift in perspective then begs the question: how should one define the extent of the system underlying an experiment? Our paper primarily aims at exposing this question rather than providing a definitive answer to it. We start by formulating a notion of relative noncontextuality for prepare-and-measure scenarios, which is simply noncontextuality with respect to an explicit reference of indistinguishability. We investigate how verdicts of relative noncontextuality depend on this choice of reference, and in the process introduce the concept of the noncontextuality graph of a prepare-and-measure scenario. We then discuss several proposals that one may appeal to in order to fix the reference to a specific choice, and relate these proposals to different conceptions of what a system really is. With this discussion, we advocate that whether or not an experiment is noncontextual is not as absolute as often perceived.

quant-ph↗

arXiv2022

Solvable Criterion for the Contextuality of any Prepare-and-Measure Scenario

Starting from arbitrary sets of quantum states and measurements, referred to as the prepare-and-measure scenario, an operationally noncontextual ontological model of the quantum statistics associated with the prepare-and-measure scenario is constructed. The operationally noncontextual ontological model coincides with standard Spekkens noncontextual ontological models for tomographically complete scenarios, while covering the non-tomographically complete case with a new notion of a reduced space, which we motivate following the guiding principles of noncontextuality. A mathematical criterion, called unit separability, is formulated as the relevant classicality criterion -- the name is inspired by the usual notion of quantum state separability. Using this criterion, we derive a new upper bound on the cardinality of the ontic space. Then, we recast the unit separability criterion as a (possibly infinite) set of linear constraints, from which we obtain two separate hierarchies of algorithmic tests to witness the non-classicality or certify the classicality of a scenario. Finally, we reformulate our results in the framework of generalized probabilistic theories and discuss the implications for simplex-embeddability in such theories.

quant-ph↗

arXiv2022

Quantum clocks are more precise than classical ones

A clock is, from an information-theoretic perspective, a system that emits information about time. One may therefore ask whether the theory of information imposes any constraints on the maximum precision of clocks. Here we show a quantum-over-classical advantage for clocks or, more precisely, the task of generating information about what time it is. The argument is based on information-theoretic considerations: we analyse how the precision of a clock scales with its size, measured in terms of the number of bits that could be stored in it. We find that a quantum clock can achieve a quadratically improved precision compared to a purely classical one of the same size.

quant-ph↗

arXiv2021

Optimal Universal Quantum Error Correction via Bounded Reference Frames

Error correcting codes with a universal set of transversal gates are a desideratum for quantum computing. Such codes, however, are ruled out by the Eastin-Knill theorem. Moreover, the theorem also rules out codes which are covariant with respect to the action of transversal unitary operations forming continuous symmetries. In this work, starting from an arbitrary code, we construct approximate codes which are covariant with respect to the entire group of local unitary gates in dimension $d$, using quantum reference frames. We show that our codes are capable of efficiently correcting different types of erasure errors. When only a small fraction of the $n$ qudits upon which the code is built are erased, our covariant code has an error that scales as $1/n^2$, which is reminiscent of the Heisenberg limit of quantum metrology. When every qudit has a chance of being erased, our covariant code has an error that scales as $1/n$. We show that the error scaling is optimal in both cases. Our approach has implications for fault-tolerant quantum computing, reference frame error correction, and the AdS-CFT duality.

quant-ph↗

arXiv2021

Measuring time with stationary quantum clocks

Time plays a fundamental role in our ability to make sense of the physical laws in the world around us. The nature of time has puzzled people -- from the ancient Greeks to the present day -- resulting in a long running debate between philosophers and physicists alike to whether time needs change to exist (the so-called relatival theory), or whether time flows regardless of change (the so-called substantival theory). One way to decide between the two is to attempt to measure the flow of time with a stationary clock, since if time were substantival, the flow of time would manifest itself in the experiment. Alas, conventional wisdom suggests that in order for a clock to function, it cannot be a static object, thus rendering this experiment seemingly impossible. Here we show, with the aid of counterfactual measurements, the surprising result that a quantum clock can measure the passage of time even while being switched off, thus lending constructive support for the substantival theory of time.

quant-ph↗

arXiv2021

Ticking-clock performance enhanced by nonclassical temporal correlations

We investigate the role of nonclassical temporal correlations in enhancing the performance of ticking clocks in a discrete-time scenario. We show that the problem of optimal models for ticking clocks is related to the violation of Leggett-Garg-type temporal inequalities formulated in terms of, possibly invasive, sequential measurements, but on a system with a bounded memory capacity. Ticking clocks inspire the derivation of a family of temporal inequalities showing a gap between classical and quantum correlations, despite involving no input. We show that quantum ticking-clock models achieving accuracy beyond the classical bound are also those violating Leggett-Garg-type temporal inequalities for finite sequences and we investigate their continuous-time limit. Interestingly, we show that optimal classical clock models in the discrete-time scenario do not have a well-defined continuous-time limit, a feature that is absent in quantum models.

quant-ph↗

arXiv2021

Autonomous Ticking Clocks from Axiomatic Principles

There are many different types of time keeping devices. We use the phrase ticking clock to describe those which -- simply put -- "tick" at approximately regular intervals. Various important results have been derived for ticking clocks, and more are in the pipeline. It is thus important to understand the underlying models on which these results are founded. The aim of this paper is to introduce a new ticking clock model from axiomatic principles that overcomes concerns in the community about the physicality of the assumptions made in previous models. The ticking clock model in [arXiv:1806.00491] achieves high accuracy, yet lacks the autonomy of the less accurate model in [10.1103/PhysRevX.7.031022]. Importantly, the model we introduce here achieves the best of both models: it retains the autonomy of [10.1103/PhysRevX.7.031022] while allowing for the high accuracies of [arXiv:1806.00491]. What is more, [10.1103/PhysRevX.7.031022] is revealed to be a special case of the new ticking clock model.

quant-ph↗

arXiv2020

Universal quantum modifications to general relativistic time dilation in delocalised clocks

The theory of relativity associates a proper time with each moving object via its world line. In quantum theory however, such well-defined trajectories are forbidden. After introducing a general characterisation of quantum clocks, we demonstrate that, in the weak-field, low-velocity limit, all "good" quantum clocks experience time dilation as dictated by general relativity when their state of motion is classical (i.e. Gaussian). For nonclassical states of motion, on the other hand, we find that quantum interference effects may give rise to a significant discrepancy between the proper time and the time measured by the clock. The universality of this discrepancy implies that it is not simply a systematic error, but rather a quantum modification to the proper time itself. We also show how the clock's delocalisation leads to a larger uncertainty in the time it measures -- a consequence of the unavoidable entanglement between the clock time and its center-of-mass degrees of freedom. We demonstrate how this lost precision can be recovered by performing a measurement of the clock's state of motion alongside its time reading.

quant-ph↗

arXiv2020

Continuous groups of transversal gates for quantum error correcting codes from finite clock reference frames

Following the introduction of the task of reference frame error correction, we show how, by using reference frame alignment with clocks, one can add a continuous Abelian group of transversal logical gates to any error-correcting code. With this we further explore a way of circumventing the no-go theorem of Eastin and Knill, which states that if local errors are correctable, the group of transversal gates must be of finite order. We are able to do this by introducing a small error on the decoding procedure that decreases with the dimension of the frames used. Furthermore, we show that there is a direct relationship between how small this error can be and how accurate quantum clocks can be: the more accurate the clock, the smaller the error; and the no-go theorem would be violated if time could be measured perfectly in quantum mechanics. The asymptotic scaling of the error is studied under a number of scenarios of reference frames and error models. The scheme is also extended to errors at unknown locations, and we show how to achieve this by simple majority voting related error correction schemes on the reference frames. In the Outlook, we discuss our results in relation to the AdS/CFT correspondence and the Page-Wooters mechanism.

quant-ph↗