Fast quantum computation at arbitrarily low energy

Jordan, Stephen P.

doi:10.1103/physreva.95.032305

Cited by 31 publications

(21 citation statements)

References 49 publications

(62 reference statements)

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“…Both these articles justify their conclusion by the fact that the work of a quantum circuit that is made of a set of standard quantum gates can be simulated by evolution with a Hamiltonian that requests less energy resources. While this is certainly useful to know for optimization of quantum gates, quantum simulators discussed in [14,15] are not complete algorithms, so the comparison could be unfair. For example, it is unclear whether a quantum simulator allows energy effective error correction strategy.…”

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Computing with a single qubit faster than the computation quantum speed limit

Sinitsyn

2018

Physics Letters A

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The possibility to save and process information in fundamentally indistinguishable states is the quantum mechanical resource that is not encountered in classical computing. I demonstrate that, if energy constraints are imposed, this resource can be used to accelerate information-processing without relying on entanglement or any other type of quantum correlations. In fact, there are computational problems that can be solved much faster, in comparison to currently used classical schemes, by saving intermediate information in nonorthogonal states of just a single qubit. There are also error correction strategies that protect such computations.Introduction. The quantum phase space of a qubit is a sphere (Fig. 1). One can discretize this space into any number of states and then apply field pulses to switch between the chosen states in an arbitrary order. In this sense, a qubit comprises the whole universe of choices for computation. For example, a qubit can work as finite automata [1] when different unitary gates act on this qubit depending on arriving digital words. However, different states of a qubit are generally not distinguishable by measurements. So, if the final quantum state encodes the result of computation, we cannot generally extract this information because we cannot distinguish this state by a measurement from other non-orthogonal possibilities reliably.For such reasons, qubits are believed to provide computational advantage over classical memory only when they are used to create purely quantum correlations, i.e., entanglement or quantum discord [2]. While very powerful algorithms have been designed based on such correlations, the degree of control over the state of many qubits that is needed to implement commercially competitive quantum computing is far from the level of the modern technology.In this note, I will argue that the ability to use nonorthogonal states for computation should be considered as the completely independent resource that is provided by quantum mechanics. With a specific example, I will show that there are computational problems for which the access to just one high quality qubit may provide speed of computation that, fundamentally, cannot be reached by a classical computer under the specified restrictions on raw resources such as memory coupling strength to control fields.The idea of this article is based on the well known observation that time-energy uncertainty relation in quantum mechanics imposes limits on computation speed at fixed power supply for classical schemes of computer operation [3,4]. Such claims are generally justified by the fact that digital computers save information in the form of clearly distinguishable states, such as 0 and 1 that encode one bit of information. Quantum mechanically, distinguishable states must be represented by orthogonal vectors that produce definitely different measurement outcomes. However, the switching time between two orthogonal quantum states is restricted from below by a fundamental computation speed limit T = h/(4∆E), where ∆E is cha...

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“…It is also unclear from Refs. [14,15] whether purely quantum correlations, such as entanglement and quantum discord, are required for energy efficiency. Purely quantum correlations are currently very hard to control even on the level of few qubits, so energy efficiency of dealing with such correlations cannot become important in the near future.…”

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confidence: 99%

Computing with a single qubit faster than the computation quantum speed limit

Sinitsyn

2018

Physics Letters A

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“…The bound is fascinating since it is simple and powerful. However, whether the computational speed is really limited by the energy considerations alone for a system was recently questioned in [3]. It was argued there that the energy alone is not sufficient to derive an upper bound on the computational speed.…”

Section: Introductionmentioning

confidence: 99%

Holographic complexity and thermodynamics of AdS black holes

Fan

Guo

2019

Phys. Rev. D

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In this paper, we relate the complexity for a holographic state to a simple gravitational object of which the growth rate at late times is equal to temperature times black hole entropy. We show that if this is correct, the thermodynamics of AdS black holes implies that for generic holographic states dual to static AdS black holes, the complexity growth rate at late times will saturate the Lloyd bound at high temperature limit. In particular, for AdS planar black holes, the result holds at lower temperatures as well. We conjecture that the complexity growth is bounded above as dC/dt ≤ αT S/π or dC/dt ≤ α T + S + − T − S − /π for black holes with an inner horizon, where α is an overall coefficient for our new proposal.The conjecture passes a number of nontrivial tests for black holes in Einstein's gravity.However, we also find that the bound may be violated in the presence of stringy corrections.

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“…As a result, one does not expect a bound like (2.16) to hold in general, and in fact one can easily find violations when simple gates are used. This was recently illustrated in the works [45,46], where arbitrarily large complexification rates are achieved in particular examples -in the latter case, in a system with one qubit only. To illustrate this point, assume we have a reference state |0 and any other state |Ψ and suppose we have unitary evolution described by…”

Section: Jhep02(2018)039mentioning

confidence: 99%

Complexity is simple!

Cottrell

2018

J. High Energ. Phys.

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In this note we investigate the role of Lloyd's computational bound in holographic complexity. Our goal is to translate the assumptions behind Lloyd's proof into the bulk language. In particular, we discuss the distinction between orthogonalizing and 'simple' gates and argue that these notions are useful for diagnosing holographic complexity. We show that large black holes constructed from series circuits necessarily employ simple gates, and thus do not satisfy Lloyd's assumptions. We also estimate the degree of parallel processing required in this case for elementary gates to orthogonalize. Finally, we show that for small black holes at fixed chemical potential, the orthogonalization condition is satisfied near the phase transition, supporting a possible argument for the Weak Gravity Conjecture first advocated in [1].

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Fast quantum computation at arbitrarily low energy

Cited by 31 publications

References 49 publications

Computing with a single qubit faster than the computation quantum speed limit

Computing with a single qubit faster than the computation quantum speed limit

Holographic complexity and thermodynamics of AdS black holes

Complexity is simple!

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