arXiv subjects

Akimasa Miyake

Publications and source records attributed to Akimasa Miyake.

At least 37 records · Page 2Linked to original sources

arXiv2018

Many-body-localization transition in a universal quantum circuit model

The dynamical generation of complex correlations in quantum many-body systems is of renewed interest in the context of quantum chaos, where the out-of-time-ordered (OTO) correlation function appears as a convenient measure of scrambling. To detect the the transition from scrambling to many-body localization, the latter of which has limited dynamical complexity and is often classically simulatable, we develop both exact and approximate methods to compute OTO correlators for arbitrary universal quantum circuits. We take advantage of the mapping of quantum circuits to the dynamics of interacting fermions in one dimension, as Gaussian time evolution supplemented by quartic interaction gates. In this framework, the OTO correlator can be calculated exactly as a superposition of exponentially many Gaussian-fermionic trajectories in the number of interaction gates. We develop a variationally-optimized, Gaussian approximation to the spatial propagation of an initially-local operator by restriction to the fastest-traveling fermionic modes, in a similar spirit as light-front computational methods in quantum field theory. We demonstrate that our method can detect the many-body localization transitions of generally time-dependent dynamics without the need for perturbatively weak interactions.

quant-ph↗

arXiv2018

Classical simulation of quantum circuits by dynamical localization: analytic results for Pauli-observable scrambling in time-dependent disorder

We extend the concept of Anderson localization, the confinement of quantum information in a spatially irregular potential, to quantum circuits. Considering matchgate circuits, generated by time-dependent spin-1/2 XY Hamiltonians, we give an analytic formula for the out-of-time-ordered correlator of a local observable, and show that it can be efficiently evaluated by a classical computer even when the explicit Heisenberg time evolution cannot. Because this quantity bounds the average error incurred by truncating the evolution to a spatially limited region, we demonstrate dynamical localization as a means for classically simulating quantum computation and give examples of localized phases under certain spatio-temporal disordered Hamiltonians.

quant-ph↗

arXiv2018

Latent Computational Complexity of Symmetry-Protected Topological Order with Fractional Symmetry

An emerging insight is that ground states of symmetry-protected topological orders (SPTO's) possess latent computational complexity in terms of their many-body entanglement. By introducing a fractional symmetry of SPTO, which requires the invariance under 3-colorable symmetries of a lattice, we prove that every renormalization fixed-point state of 2D $(\mathbb{Z}_2)^m$ SPTO with fractional symmetry can be utilized for universal quantum computation using only Pauli measurements, as long as it belongs to a nontrivial 2D SPTO phase. Our infinite family of fixed-point states may serve as a base model to demonstrate the idea of a "quantum computational phase" of matter, whose states share universal computational complexity ubiquitously.

quant-ph↗

arXiv2017

Quantum supremacy in constant-time measurement-based computation: A unified architecture for sampling and verification

While quantum speed-up in solving certain decision problems by a fault-tolerant universal quantum computer has been promised, a timely research interest includes how far one can reduce the resource requirement to demonstrate a provable advantage in quantum devices without demanding quantum error correction, which is crucial for prolonging the coherence time of qubits. We propose a model device made of locally-interacting multiple qubits, designed such that simultaneous single-qubit measurements on it can output probability distributions whose average-case sampling is classically intractable, under similar assumptions as the sampling of non-interacting bosons and instantaneous quantum circuits. Notably, in contrast to these previous unitary-based realizations, our measurement-based implementation has two distinctive features. (i) Our implementation involves no adaptation of measurement bases, leading output probability distributions to be generated in constant time, independent of the system size. Thus, it could be implemented in principle without quantum error correction. (ii) Verifying the classical intractability of our sampling is done by changing the Pauli measurement bases only at certain output qubits. Our usage of random commuting quantum circuits in place of computationally universal circuits allows a unique unification of sampling and verification, so that they require the same physical resource requirements in contrast to the more demanding verification protocols seen elsewhere in the literature.

quant-ph↗

arXiv2017

Robust symmetry-protected metrology with the Haldane phase

We propose a metrology scheme that is made robust to a wide range of noise processes by using the passive, error-preventing properties of symmetry-protected topological phases. The so-called fractionalized edge mode of an antiferromagnetic Heisenberg spin-1 chain in a rotationally-symmetric Haldane phase can be used to measure the direction of an unknown electric field, by exploiting the way in which the field direction reduces the symmetry of the chain. Specifically, the direction of the field is registered in the holonomy under an adiabatic sensing protocol, and the degenerate fractionalized edge mode is protected through this process by the remaining reduced symmetry. We illustrate the scheme with respect to a potential realization by Rydberg dressed atoms.

quant-ph↗

arXiv2016

Hierarchy of universal entanglement in 2D measurement-based quantum computation

Measurement-based quantum computation (MQC) is a paradigm for studying quantum computation using many-body entanglement and single-qubit measurements. While MQC has inspired wide-ranging discoveries throughout quantum information, our understanding of the general principles underlying MQC seems to be biased by its historical reliance upon the archetypal 2D cluster state. Here, we utilize recent advances in the subject of symmetry-protected topological order (SPTO) to introduce a novel MQC resource state, whose physical and computational behavior differs fundamentally from the cluster state. We show that, in sharp contrast to the cluster state, our state enables universal quantum computation using only measurements of single-qubit Pauli X, Y, and Z operators. This novel computational feature is related to the "genuine" 2D SPTO possessed by our state, and which is absent in the cluster state. Our concrete connection between the latent computational complexity of many-body systems and macroscopic quantum orders may find applications in quantum many-body simulation for benchmarking classically intractable complexity.

quant-ph↗

arXiv2016

How an autonomous quantum Maxwell demon can harness correlated information

We study an autonomous quantum system which exhibits refrigeration under an information-work trade-off like a Maxwell demon. The system becomes correlated as a single "demon" qubit interacts sequentially with memory qubits while in contact with two heat reservoirs of different temperatures. Using strong subadditivity of the von Neumann entropy, we derive a global Clausius inequality to show thermodynamic advantages from access to correlated information. It is demonstrated, in a matrix product density operator formalism, that our demon can simultaneously realize refrigeration against a thermal gradient and erasure of information from its memory, which is impossible without correlations. The phenomenon can be even enhanced by the presence of quantum coherence.

quant-ph↗

arXiv2015

Jordan-Wigner formalism for arbitrary 2-input 2-output matchgates and their classical simulation

In Valiant's matchgate theory, 2-input 2-output matchgates are 4x4 matrices that satisfy ten so-called matchgate identities. We prove that the set of all such matchgates (including non-unitary and non-invertible ones) coincides with the topological closure of the set of all matrices obtained as exponentials of linear combinations of the 2-qubit Jordan-Wigner (JW) operators and their quadratic products, extending a previous result of Knill. In Valiant's theory, outputs of matchgate circuits can be classically computed in poly-time. Via the JW formalism, Terhal & DiVincenzo and Knill established a relation of a unitary class of these circuits to the efficient simulation of non-interacting fermions. We describe how the JW formalism may be used to give an efficient simulation for all cases in Valiant's simulation theorem, which in particular includes the case of non-interacting fermions generalised to allow arbitrary 1-qubit gates on the first line at any stage in the circuit. Finally we give an exposition of how these simulation results can be alternatively understood from some basic Lie algebra theory, in terms of a formalism introduced by Somma et al.

quant-ph↗

arXiv2015

Resource quality of a symmetry-protected topologically ordered phase for quantum computation

We investigate entanglement naturally present in the 1D topologically ordered phase protected with the on-site symmetry group of an octahedron as a potential resource for teleportation-based quantum computation. We show that, as long as certain characteristic lengths are finite, all its ground states have the capability to implement any unit-fidelity one-qubit gate operation asymptotically as a key computational building block. This feature is intrinsic to the entire phase, in that perfect gate fidelity coincides with perfect string order parameters under a state-insensitive renormalization procedure. Our approach may pave the way toward a novel program to classify quantum many-body systems based on their operational use for quantum information processing.

quant-ph↗

arXiv2013

Holonomic quantum computing in symmetry-protected ground states of spin chains

While solid-state devices offer naturally reliable hardware for modern classical computers, thus far quantum information processors resemble vacuum tube computers in being neither reliable nor scalable. Strongly correlated many body states stabilized in topologically ordered matter offer the possibility of naturally fault tolerant computing, but are both challenging to engineer and coherently control and cannot be easily adapted to different physical platforms. We propose an architecture which achieves some of the robustness properties of topological models but with a drastically simpler construction. Quantum information is stored in the symmetry-protected degenerate ground states of spin-1 chains, while quantum gates are performed by adiabatic non-Abelian holonomies using only single-site fields and nearest-neighbor couplings. Gate operations respect the symmetry, and so inherit some protection from noise and disorder from the symmetry-protected ground states.

quant-ph↗

arXiv2011

Entropic time endowed in quantum correlations

A possible mechanism of time is formulated by developing an idea of time replaced by quantum correlations, with the aid of modern quantum information theory. We invent a microscopic model, where correlations of a closed system are steadily read out as internal, quantum clocks that define time via their relative phases. The model could realize emergent time evolutions which exhibit unitarity of quantum theory, while its underlying process is driven entropically. The key quantity turns out to be the amount of accessible information about the clocks recording past events. By postulating the so-called data-processing inequality (or strong subadditivity of entropy) as a fundamental, physical limitation about how information decays, we propose that conditional entropy about this past information should be constrained to be a positive constant. The proposal implies a holographic property of this conditional entropy in an analogous manner with the area law of entanglement entropy.

quant-ph↗

arXiv2011

Quantum computational capability of a 2D valence bond solid phase

Quantum phases of naturally-occurring systems exhibit distinctive collective phenomena as manifestation of their many-body correlations, in contrast to our persistent technological challenge to engineer at will such strong correlations artificially. Here we show theoretically that quantum correlations exhibited in the two-dimensional valence bond solid phase of a quantum antiferromagnet, modeled by Affleck, Kennedy, Lieb, and Tasaki as a precursor of spin liquids and topological orders, are sufficiently complex yet structured enough to simulate universal quantum computation when every single spin can be measured individually. This unveils that an intrinsic complexity of naturally-occurring 2D quantum systems -- which has been a long-standing challenge for traditional computers -- could be tamed as a computationally valuable resource, even if we are limited not to create newly entanglement during computation. Our constructive protocol leverages a novel way to herald the correlations suitable for deterministic quantum computation through a random sampling, and may be extensible to other ground states of various 2D valence bond phases beyond the AKLT state.

quant-ph↗

arXiv2010

Universal quantum computer from a quantum magnet

We show that a local Hamiltonian of spin-3/2 particles with only two-body nearest-neighbor Affleck-Kennedy-Lieb-Tasaki and exchange-type interactions has an unique ground state, which can be used to implement universal quantum computation merely with single-spin measurements. We prove that the Hamiltonian is gapped, independent of the system size. Our result provides a further step towards utilizing systems with condensed matter-type interactions for measurement-based quantum computation.

quant-ph↗

arXiv2010

Quantum computational renormalization in the Haldane phase

Single-spin measurements on the ground state of an interacting spin lattice can be used to perform a quantum computation. We show how such measurements can mimic renormalization group transformations and remove the short-ranged variations of the state that can reduce the fidelity of a computation. This suggests that the quantum computational ability of a spin lattice could be a robust property of a quantum phase. We illustrate our idea with the ground state of a spin-1 chain, which can serve as a quantum computational wire not only at the Affleck-Kennedy-Lieb-Tasaki point, but within the rotationally-invariant Haldane phase.

quant-ph↗

arXiv2010

Quantum computation on the edge of a symmetry-protected topological order

We elaborate the idea of quantum computation through measuring the correlation of a gapped ground state, while the bulk Hamiltonian is utilized to stabilize the resource. A simple computational primitive, by pulling out a single spin adiabatically from the bulk followed by its measurement, is shown to make any ground state of the one-dimensional isotropic Haldane phase useful ubiquitously as a quantum logical wire. The primitive is compatible with certain discrete symmetries that protect this topological order, and the antiferromagnetic Heisenberg spin-1 finite chain is practically available. Our approach manifests a holographic principle in that the logical information of a universal quantum computer can be written and processed perfectly on the edge state (i.e., boundary) of the system, supported by the persistent entanglement from the bulk even when the ground state and its evolution cannot be exactly analyzed.

quant-ph↗

arXiv2010

Matchgate and space-bounded quantum computations are equivalent

Matchgates are an especially multiflorous class of two-qubit nearest neighbour quantum gates, defined by a set of algebraic constraints. They occur for example in the theory of perfect matchings of graphs, non-interacting fermions, and one-dimensional spin chains. We show that the computational power of circuits of matchgates is equivalent to that of space-bounded quantum computation with unitary gates, with space restricted to being logarithmic in the width of the matchgate circuit. In particular, for the conventional setting of polynomial-sized (logarithmic-space generated) families of matchgate circuits, known to be classically simulatable, we characterise their power as coinciding with polynomial-time and logarithmic-space bounded universal unitary quantum computation.

quant-ph↗

arXiv2008

Matchgates and classical simulation of quantum circuits

Let G(A,B) denote the 2-qubit gate which acts as the 1-qubit SU(2) gates A and B in the even and odd parity subspaces respectively, of two qubits. Using a Clifford algebra formalism we show that arbitrary uniform families of circuits of these gates, restricted to act only on nearest neighbour (n.n.) qubit lines, can be classically efficiently simulated. This reproduces a result originally proved by Valiant using his matchgate formalism, and subsequently related by others to free fermionic physics. We further show that if the n.n. condition is slightly relaxed, to allowing the same gates to act only on n.n. and next-n.n. qubit lines, then the resulting circuits can efficiently perform universal quantum computation. From this point of view, the gap between efficient classical and quantum computational power is bridged by a very modest use of a seemingly innocuous resource (qubit swapping). We also extend the simulation result above in various ways. In particular, by exploiting properties of Clifford operations in conjunction with the Jordan-Wigner representation of a Clifford algebra, we show how one may generalise the simulation result above to provide further classes of classically efficiently simulatable quantum circuits, which we call Gaussian quantum circuits.

quant-ph↗

arXiv2008

Measurement-based quantum computer in the gapped ground state of a two-body Hamiltonian

We propose a scheme for a ground-code measurement-based quantum computer, which enjoys two major advantages. First, every logical qubit is encoded in the gapped degenerate ground subspace of a spin-1 chain with nearest-neighbor two-body interactions, so that it equips built-in robustness against noise. Second, computation is processed by single-spin measurements along multiple chains dynamically coupled on demand, so as to keep teleporting only logical information into a gap-protected ground state of the residual chains after the interactions with spins to be measured are turned off. We describe implementations using trapped atoms or polar molecules in an optical lattice, where the gap is expected to be as large as 0.2 kHz or 4.8 kHz respectively.

quant-ph↗