arXiv subjects

John Preskill

Publications and source records attributed to John Preskill.

At least 55 records · Page 3Linked to original sources

arXiv2024

Collisions of false-vacuum bubble walls in a quantum spin chain

We simulate, using nonperturbative methods, the real-time dynamics of small bubbles of "false vacuum" in a quantum spin chain near criticality, where the low-energy physics is described by a relativistic (1+1)-dimensional quantum field theory. We consider bubbles whose walls are kink and antikink quasiparticle excitations, so that wall collisions are kink-antikink scattering events. To construct these bubbles in the presence of strong correlations, we extend a recently proposed matrix product state (MPS) ansatz for quasiparticle wavepackets. We simulate dynamics within a window of about 1000 spins embedded in an infinite chain at energies of up to about 5 times the mass gap. By choosing the wavepacket width and the bubble size appropriately, we avoid strong lattice effects and observe relativistic kink-antikink collisions. We use the MPS quasiparticle ansatz to detect scattering outcomes. (i) In the Ising model, with transverse and longitudinal fields, we do not observe particle production despite nonintegrability (supporting recent observations of nonthermalizing states in this model). (ii) Switching on an additional interaction, we see production of confined and unconfined particle pairs. We characterize the amount of entanglement generated as a function of energy and time and conclude that our classical simulation methods will ultimately fail as these increase. We anticipate that kink-antikink scattering in 1+1 dimensions will be an instructive benchmark problem for future quantum computers and analog quantum simulators.

quant-ph↗

arXiv2024

Resilience of the surface code to error bursts

Quantum error correction works effectively only if the error rate of gate operations is sufficiently low. However, some rare physical mechanisms can cause a temporary increase in the error rate that affects many qubits; examples include ionizing radiation in superconducting hardware and large deviations in the global control of atomic systems. We refer to such rare transient spikes in the gate error rate as error bursts. In this work, we investigate the resilience of the surface code to generic error bursts. We assume that, after appropriate mitigation strategies, the spike in the error rate lasts for only a single syndrome extraction cycle; we also assume that the enhanced error rate is uniform across the code block. Under these assumptions, and for a circuit-level depolarizing noise model, we perform Monte Carlo simulations to determine the regime in burst error rate and background error rate for which the memory time becomes arbitrarily long as the code block size grows. Our results indicate that suitable hardware mitigation methods combined with standard decoding methods may suffice to protect against transient error bursts in the surface code.

quant-ph↗

arXiv2024

Efficient soft-output decoders for the surface code

Decoders that provide an estimate of the probability of a logical failure conditioned on the error syndrome ("soft-output decoders") can reduce the overhead cost of fault-tolerant quantum memory and computation. In this work, we construct efficient soft-output decoders for the surface code derived from the Minimum-Weight Perfect Matching and Union-Find decoders. We show that soft-output decoding can improve the performance of a "hierarchical code," a concatenated scheme in which the inner code is the surface code, and the outer code is a high-rate quantum low-density parity-check code. Alternatively, the soft-output decoding can improve the reliability of fault-tolerant circuit sampling by flagging those runs that should be discarded because the probability of a logical error is intolerably large.

quant-ph↗

arXiv2024

Stochastic waveform estimation at the fundamental quantum limit

Although measuring the deterministic waveform of a weak classical force is a well-studied problem, estimating a random waveform, such as the spectral density of a stochastic signal field, is much less well-understood despite it being a widespread task at the frontier of experimental physics. State-of-the-art precision sensors of random forces must account for the underlying quantum nature of the measurement, but the optimal quantum protocol for interrogating such linear sensors is not known. We derive the fundamental precision limit, the extended channel quantum Cramér-Rao bound, and the optimal protocol that attains it. In the experimentally relevant regime where losses dominate, we prove that non-Gaussian state preparation and measurements are required for optimality. We discuss how this non-Gaussian protocol could improve searches for signatures of quantum gravity, stochastic gravitational waves, and axionic dark matter.

quant-ph↗

arXiv2024

Certifying almost all quantum states with few single-qubit measurements

Certifying that an n-qubit state synthesized in the lab is close to the target state is a fundamental task in quantum information science. However, existing rigorous protocols either require deep quantum circuits or exponentially many single-qubit measurements. In this work, we prove that almost all n-qubit target states, including those with exponential circuit complexity, can be certified from only O(n^2) single-qubit measurements. This result is established by a new technique that relates certification to the mixing time of a random walk. Our protocol has applications for benchmarking quantum systems, for optimizing quantum circuits to generate a desired target state, and for learning and verifying neural networks, tensor networks, and various other representations of quantum states using only single-qubit measurements. We show that such verified representations can be used to efficiently predict highly non-local properties that would otherwise require an exponential number of measurements. We demonstrate these applications in numerical experiments with up to 120 qubits, and observe advantage over existing methods such as cross-entropy benchmarking (XEB).

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

Local minima in quantum systems

Finding ground states of quantum many-body systems is known to be hard for both classical and quantum computers. As a result, when Nature cools a quantum system in a low-temperature thermal bath, the ground state cannot always be found efficiently. Instead, Nature finds a local minimum of the energy. In this work, we study the problem of finding local minima in quantum systems under thermal perturbations. While local minima are much easier to find than ground states, we show that finding a local minimum is computationally hard for classical computers, even when the task is to output a single-qubit observable at any local minimum. In contrast, we prove that a quantum computer can always find a local minimum efficiently using a thermal gradient descent algorithm that mimics the cooling process in Nature. To establish the classical hardness of finding local minima, we consider a family of two-dimensional Hamiltonians such that any problem solvable by polynomial-time quantum algorithms can be reduced to finding ground states of these Hamiltonians. We prove that for such Hamiltonians, all local minima are global minima. Therefore, assuming quantum computation is more powerful than classical computation, finding local minima is classically hard and quantumly easy.

quant-ph↗

arXiv2023

Emergent Quantum Mechanics at the Boundary of a Local Classical Lattice Model

We formulate a conceptually new model in which quantum mechanics emerges from classical mechanics. Given a local Hamiltonian $H$ acting on $n$ qubits, we define a local classical model with an additional spatial dimension whose boundary dynamics is approximately -- but to arbitrary precision -- described by Schrödinger's equation and $H$. The bulk consists of a lattice of classical bits that propagate towards the boundary through a circuit of stochastic matrices. The bits reaching the boundary are governed by a probability distribution whose deviation from the uniform distribution can be interpreted as the quantum-mechanical wavefunction. Bell nonlocality is achieved because information can move through the bulk much faster than the boundary speed of light. We analytically estimate how much the model deviates from quantum mechanics, and we validate these estimates using computer simulations.

quant-ph↗

arXiv2023

Enhanced estimation of quantum properties with common randomized measurements

We present a technique for enhancing the estimation of quantum state properties by incorporating approximate prior knowledge about the quantum state of interest. This method involves performing randomized measurements on a quantum processor and comparing the results with those obtained from a classical computer that stores an approximation of the quantum state. We provide unbiased estimators for expectation values of multi-copy observables and present performance guarantees in terms of variance bounds which depend on the prior knowledge accuracy. We demonstrate the effectiveness of our approach through numerical experiments estimating polynomial approximations of the von Neumann entropy and quantum state fidelities.

quant-ph↗

arXiv2023

Learning to predict arbitrary quantum processes

We present an efficient machine learning (ML) algorithm for predicting any unknown quantum process $\mathcal{E}$ over $n$ qubits. For a wide range of distributions $\mathcal{D}$ on arbitrary $n$-qubit states, we show that this ML algorithm can learn to predict any local property of the output from the unknown process~$\mathcal{E}$, with a small average error over input states drawn from $\mathcal{D}$. The ML algorithm is computationally efficient even when the unknown process is a quantum circuit with exponentially many gates. Our algorithm combines efficient procedures for learning properties of an unknown state and for learning a low-degree approximation to an unknown observable. The analysis hinges on proving new norm inequalities, including a quantum analogue of the classical Bohnenblust-Hille inequality, which we derive by giving an improved algorithm for optimizing local Hamiltonians. Numerical experiments on predicting quantum dynamics with evolution time up to $10^6$ and system size up to $50$ qubits corroborate our proof. Overall, our results highlight the potential for ML models to predict the output of complex quantum dynamics much faster than the time needed to run the process itself.

quant-ph↗

arXiv2023

Complementarity and the unitarity of the black hole $S$-matrix

Recently, Akers et al. proposed a non-isometric holographic map from the interior of a black hole to its exterior. Within this model, we study properties of the black hole $S$-matrix, which are in principle accessible to observers who stay outside the black hole. Specifically, we investigate a scenario in which an infalling agent interacts with radiation both outside and inside the black hole. Because the holographic map involves postselection, the unitarity of the $S$-matrix is not guaranteed in this scenario, but we find that unitarity is satisfied to very high precision if suitable conditions are met. If the internal black hole dynamics is described by a pseudorandom unitary transformation, and if the operations performed by the infaller have computational complexity scaling polynomially with the black hole entropy, then the $S$-matrix is unitary up to corrections that are superpolynomially small in the black hole entropy. Furthermore, while in principle quantum computation assisted by postselection can be very powerful, we find under similar assumptions that the $S$-matrix of an evaporating black hole has polynomial computational complexity.

hep-th↗

arXiv2023

Quantum computing 40 years later

Forty years ago, Richard Feynman proposed harnessing quantum physics to build a more powerful kind of computer. Realizing Feynman's vision is one of the grand challenges facing 21st century science and technology. In this article, we'll recall Feynman's contribution that launched the quest for a quantum computer, and assess where the field stands 40 years later.

quant-ph↗

arXiv2023

Improved machine learning algorithm for predicting ground state properties

Finding the ground state of a quantum many-body system is a fundamental problem in quantum physics. In this work, we give a classical machine learning (ML) algorithm for predicting ground state properties with an inductive bias encoding geometric locality. The proposed ML model can efficiently predict ground state properties of an $n$-qubit gapped local Hamiltonian after learning from only $\mathcal{O}(\log(n))$ data about other Hamiltonians in the same quantum phase of matter. This improves substantially upon previous results that require $\mathcal{O}(n^c)$ data for a large constant $c$. Furthermore, the training and prediction time of the proposed ML model scale as $\mathcal{O}(n \log n)$ in the number of qubits $n$. Numerical experiments on physical systems with up to 45 qubits confirm the favorable scaling in predicting ground state properties using a small training dataset.

quant-ph↗

arXiv2022

Is there evidence for exponential quantum advantage in quantum chemistry?

The idea to use quantum mechanical devices to simulate other quantum systems is commonly ascribed to Feynman. Since the original suggestion, concrete proposals have appeared for simulating molecular and materials chemistry through quantum computation, as a potential ``killer application''. Indications of potential exponential quantum advantage in artificial tasks have increased interest in this application, thus, it is critical to understand the basis for potential exponential quantum advantage in quantum chemistry. Here we gather the evidence for this case in the most common task in quantum chemistry, namely, ground-state energy estimation. We conclude that evidence for such an exponential advantage across chemical space has yet to be found. While quantum computers may still prove useful for quantum chemistry, it may be prudent to assume exponential speedups are not generically available for this problem.

physics.chem-ph↗

arXiv2022

Provably efficient machine learning for quantum many-body problems

Classical machine learning (ML) provides a potentially powerful approach to solving challenging quantum many-body problems in physics and chemistry. However, the advantages of ML over more traditional methods have not been firmly established. In this work, we prove that classical ML algorithms can efficiently predict ground state properties of gapped Hamiltonians in finite spatial dimensions, after learning from data obtained by measuring other Hamiltonians in the same quantum phase of matter. In contrast, under widely accepted complexity theory assumptions, classical algorithms that do not learn from data cannot achieve the same guarantee. We also prove that classical ML algorithms can efficiently classify a wide range of quantum phases of matter. Our arguments are based on the concept of a classical shadow, a succinct classical description of a many-body quantum state that can be constructed in feasible quantum experiments and be used to predict many properties of the state. Extensive numerical experiments corroborate our theoretical results in a variety of scenarios, including Rydberg atom systems, 2D random Heisenberg models, symmetry-protected topological phases, and topologically ordered phases.

quant-ph↗

arXiv2022

Provably accurate simulation of gauge theories and bosonic systems

Quantum many-body systems involving bosonic modes or gauge fields have infinite-dimensional local Hilbert spaces which must be truncated to perform simulations of real-time dynamics on classical or quantum computers. To analyze the truncation error, we develop methods for bounding the rate of growth of local quantum numbers such as the occupation number of a mode at a lattice site, or the electric field at a lattice link. Our approach applies to various models of bosons interacting with spins or fermions, and also to both abelian and non-abelian gauge theories. We show that if states in these models are truncated by imposing an upper limit $Λ$ on each local quantum number, and if the initial state has low local quantum numbers, then an error at most $ε$ can be achieved by choosing $Λ$ to scale polylogarithmically with $ε^{-1}$, an exponential improvement over previous bounds based on energy conservation. For the Hubbard-Holstein model, we numerically compute a bound on $Λ$ that achieves accuracy $ε$, obtaining significantly improved estimates in various parameter regimes. We also establish a criterion for truncating the Hamiltonian with a provable guarantee on the accuracy of time evolution. Building on that result, we formulate quantum algorithms for dynamical simulation of lattice gauge theories and of models with bosonic modes; the gate complexity depends almost linearly on spacetime volume in the former case, and almost quadratically on time in the latter case. We establish a lower bound showing that there are systems involving bosons for which this quadratic scaling with time cannot be improved. By applying our result on the truncation error in time evolution, we also prove that spectrally isolated energy eigenstates can be approximated with accuracy $ε$ by truncating local quantum numbers at $Λ=\textrm{polylog}(ε^{-1})$.

quant-ph↗

arXiv2022

The Physics of Quantum Information

Rapid ongoing progress in quantum information science makes this an apt time for a Solvay Conference focused on The Physics of Quantum Information. Here I review four intertwined themes encompassed by this topic: Quantum computer science, quantum hardware, quantum matter, and quantum gravity. Though the time scale for broad practical impact of quantum computation is still uncertain, in the near future we can expect noteworthy progress toward scalable fault-tolerant quantum computing, and discoveries enabled by programmable quantum simulators. In the longer term, controlling highly complex quantum matter will open the door to profound scientific advances and powerful new technologies.

quant-ph↗

arXiv2022

Foundations for learning from noisy quantum experiments

Understanding what can be learned from experiments is central to scientific progress. In this work, we use a learning-theoretic perspective to study the task of learning physical operations in a quantum machine when all operations (state preparation, dynamics, and measurement) are a priori unknown. We prove that, without any prior knowledge, if one can explore the full quantum state space by composing the operations, then every operation can be learned. When one cannot explore the full state space but all operations are approximately known and noise in Clifford gates is gate-independent, we find an efficient algorithm for learning all operations up to a single unlearnable parameter characterizing the fidelity of the initial state. For learning a noise channel on Clifford gates to a fixed accuracy, our algorithm uses quadratically fewer experiments than previously known protocols. Under more general conditions, the true description of the noise can be unlearnable; for example, we prove that no benchmarking protocol can learn gate-dependent Pauli noise on Clifford+T gates even under perfect state preparation and measurement. Despite not being able to learn the noise, we show that a noisy quantum computer that performs entangled measurements on multiple copies of an unknown state can yield a large advantage in learning properties of the state compared to a noiseless device that measures individual copies and then processes the measurement data using a classical computer. Concretely, we prove that noisy quantum computers with two-qubit gate error rate $ε$ can achieve a learning task using $N$ copies of the state, while $N^{Ω(1/ε)}$ copies are required classically.

quant-ph↗