Fast quantum computation at arbitrarily low energy

  title={Fast quantum computation at arbitrarily low energy},
  author={Stephen P. Jordan},
  journal={Physical Review A},
  • S. Jordan
  • Published 4 January 2017
  • Physics
  • Physical Review A
One version of the energy-time uncertainty principle states that the minimum time $T_{\perp}$ for a quantum system to evolve from a given state to any orthogonal state is $h/(4 \Delta E)$ where $\Delta E$ is the energy uncertainty. A related bound called the Margolus-Levitin theorem states that $T_{\perp} \geq h/(2 E)$ where E is the expectation value of energy and the ground energy is taken to be zero. Many subsequent works have interpreted $T_{\perp}$ as defining a minimal time for an… Expand

Figures from this paper

Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
One of the most widely known building blocks of modern physics is Heisenberg's indeterminacy principle. Among the different statements of this fundamental property of the full quantum mechanicalExpand
Computing with a single qubit faster than the computation quantum speed limit
Abstract The possibility to save and process information in fundamentally indistinguishable states is the quantum mechanical resource that is not encountered in classical computing. I demonstrateExpand
Localizing and excluding quantum information; or, how to share a quantum secret in spacetime
This work defines and analyzes the localize-exclude task, in which a quantum system must be localized to a collection of authorized regions while also being excluded from a set of unauthorized regions, and proposes a cryptographic application of these tasks which is called party-independent transfer. Expand
Toward simulating superstring/M-theory on a quantum computer
Abstract We present a novel framework for simulating matrix models on a quantum computer. Supersymmetric matrix models have natural applications to superstring/M-theory and gravitational physics, inExpand
Holographic complexity and thermodynamics of AdS black holes
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 thatExpand
On the Noether charge and the gravity duals of quantum complexity
A bstractThe physical relevance of the thermodynamic volumes of AdS black holes to the gravity duals of quantum complexity was recently argued by Couch et al. In this paper, by generalizing theExpand
Improving post-quantum cryptography through cryptanalysis
Each of the three articles raises the security estimate of a cryptosystem by showing that some attack is less effective than was previously believed and reduces the cost of using a protocol by letting the user choose smaller (or more efficient) parameters at a fixed level of security. Expand
Complexity is simple!
A bstractIn 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. InExpand
Quantum cryptanalysis in the RAM model: Claw-finding attacks on SIKE
These models of computation that enable direct comparisons between classical and quantum algorithms are introduced and the relevance of these models to cryptanalysis is demonstrated by revisiting, and increasing, the security estimates for the Supersingular Isogeny Diffie–Hellman (SIDH) and Superserpine Key Encapsulation (SIKE) schemes. Expand
Assessment of Quantum Threat To Bitcoin and Derived Cryptocurrencies
By benchmarking the speed of circuits and the time for quantum addition on quantum computers the authors can determine when there is a potential threat to a specific cryptocurrency. Expand


Fast-forwarding of Hamiltonians and exponentially precise measurements
A computational version of the TEUR (cTEUR), in which Δt is replaced by the computational complexity of simulating the measurement, is proposed, which initiates a rigorous theory of efficiency versus accuracy in energy measurements using computational complexity language. Expand
Fundamental limit on the rate of quantum dynamics: the unified bound is tight.
The fundamental limit of the operation rate of any information processing system is established: for any values of DeltaE and E, there exists a one-parameter family of initial states that can approach the bound arbitrarily close when the parameter approaches its limit. Expand
On the Interpretation of Energy as the Rate of Quantum Computation
  • M. Frank
  • Physics, Computer Science
  • Quantum Inf. Process.
  • 2005
This paper explores the precise nature of the connection between the energy of a quantum system and the difficulty of any specific quantum or classical computational operation, and calculates its difficulty, defined as the minimum effort required to perform that operation on a worst-case input state. Expand
Universal upper bound on the entropy-to-energy ratio for bounded systems
We present evidence for the existence of a universal upper bound of magnitude $\frac{2\ensuremath{\pi}R}{\ensuremath{\hbar}c}$ to the entropy-to-energy ratio $\frac{S}{E}$ of an arbitrary system ofExpand
Spectral Gap Amplification
It is shown that a quadratic spectral gap amplification is possible when $H$ satisfies a frustration-free property and give $H'$ for these cases, which results in quantum speedups for optimization problems. Expand
Universal two-body-Hamiltonian quantum computing
We present a Hamiltonian quantum computation scheme universal for quantum computation (BQP). Our Hamiltonian is a sum of a polynomial number (in the number of gates L in the quantum circuit) ofExpand
How fast can a quantum state change with time?
  • Pfeifer
  • Physics, Medicine
  • Physical review letters
  • 1993
Lower and upper bounds are derived for the decay and transitions of quantum states, evolving under a time-dependent Hamiltonian, in terms of the energy uncertainty of the initial and final state. TheExpand
Quantum Algorithms for Quantum Field Theories
A quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions in spacetime of four and fewer dimensions is developed and achieves exponential speedup over the fastest known classical algorithm. Expand
Geometry of quantum evolution.
It is shown that the integral of the uncertainty of energy with respect to time is independent of the particular Hamiltonian used to transport the quantum system along a given curve in the projective Hilbert space, which gives a new time-energy uncertainty principle. Expand
Looking at Nature as a Computer
Although not always identified as such, information has been a fundamental quantity in Physics since the advent of Statistical Mechanics, which recognized “counting states” as the fundamentalExpand