The maximum speed of dynamical evolution

Margolus, Norman; Levitin, Lev B.

doi:10.1016/s0167-2789(98)00054-2

Cited by 869 publications

(1,037 citation statements)

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“…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.…”

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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 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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confidence: 99%

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

Sinitsyn

2018

Physics Letters A

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“…Based on this premise, Lloyd [23] presented a fundamental limitation to how fast quantum computers can be. Using the Margolus-Levitin [24] theorem he notes that in order to perform a computation in a time δT one needs to expend at least an energy E ≥ πh/(2∆T ). As a consequence, a system with an average energy E can perform a maximum of n = 2E/(πh) operations per second.…”

Section: Quantum Computingmentioning

confidence: 99%

Fundamental decoherence from quantum gravity: a pedagogical review

2007

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We present a discussion of the fundamental loss of unitarity that appears in quantum mechanics due to the use of a physical apparatus to measure time. This induces a decoherence effect that is independent of any interaction with the environment and appears in addition to any usual environmental decoherence. The discussion is framed self consistently and aimed to general physicists. We derive the modified Schrödinger equation that arises in quantum mechanics with real clocks and discuss the theoretical and potential experimental implications of this process of decoherence.

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“…A natural measure for the 'speed' of quantum evolution is provided by the time interval τ that a given initial state |ψ(t 0 ) takes to evolve into an orthogonal state [11,31],…”

Section: Speed Of Evolutionmentioning

confidence: 99%

“…Another example is provided by an interesting relationship between entanglement and the time evolution of composite quantum systems that has recently been established [11][12][13][14]: quantum entanglement enhances the 'speed' of evolution of certain quantum states, as measured by the time needed to reach an orthogonal state. The problem of the 'speed' of quantum evolution has been the focus of considerable interest recently, because of its relevance in connection with the physical limits imposed by the basic laws of quantum mechanics on the speed of information processing and information transmission [31][32][33][34]. When processing information it is sensible to expect the output state of the computer device to be reasonably distinct from the input state [31].…”

Section: Introductionmentioning

confidence: 99%

Entanglement and the speed of evolution of multi-partite quantum systems

Zander¹,

Plastino²,

Casas³

2007

J. Phys. A: Math. Theor.

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There exists an interesting relationship between entanglement and the time evolution of composite quantum systems: quantum entanglement enhances the 'speed' of evolution of certain quantum states, as measured by the time needed to reach an orthogonal state. Previous research done on this subject has been focused upon comparing extreme cases (highly entangled states versus separable states) or upon bi-partite systems. In the present contribution we explore the aforementioned connection (between entanglement and time evolution) in the cases of two-qubits and N-qubits systems, taking into account states of intermediate entanglement. In particular, we investigate a family of energetically symmetric states of low entanglement that saturate the quantum speed bound. We show that, as the number of qubits increases, very little entanglement is needed to reach the quantum speed limit.

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The maximum speed of dynamical evolution

Cited by 869 publications

References 18 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

Fundamental decoherence from quantum gravity: a pedagogical review

Entanglement and the speed of evolution of multi-partite quantum systems

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