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This review article summarizes the requirement of low temperature conditions in existing experimental approaches to quantum computation and quantum simulation.
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Vibrational degrees of freedom in trapped-ion systems have recently been gaining attention as a quantum resource, beyond the role as a mediator for entangling quantum operations on internal degrees of freedom, because of the large available Hilbert space. The vibrational modes can be represented as quantum harmonic oscillators and thus offer a Hilbert space with infinite dimension. Here we review recent theoretical and experimental progress in the coherent manipulation of the vibrational modes, including bosonic encoding schemes in quantum information, reliable and efficient measurement techniques, and quantum operations that allow various quantum simulations and quantum computation algorithms. We describe experiments using the vibrational modes, including the preparation of non-classical states, molecular vibronic sampling, and applications in quantum thermodynamics. We finally discuss the potential prospects and challenges of trapped-ion vibrational-mode quantum information processing.
When calculating the overhead of a quantum algorithm made fault-tolerant using the surface code, many previous works have used defects and braids for logical qubit storage and state distillation. In this work, we show that lattice surgery reduces the storage overhead by over a factor of 4, and the distillation overhead by nearly a factor of 5, making it possible to run algorithms with $10^8$ T gates using only $3.7times 10^5$ physical qubits capable of executing gates with error $psim 10^{-3}$. These numbers strongly suggest that defects and braids in the surface code should be deprecated in favor of lattice surgery.
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 elementary computational operation and correspondingly a fundamental limit on clock speed determined by a systems energy. Here we present local time-independent Hamiltonians in which computational clock speed becomes arbitrarily large relative to E and $Delta E$ as the number of computational steps goes to infinity. We argue that energy considerations alone are not sufficient to obtain an upper bound on computational speed, and that additional physical assumptions such as limits to information density and information transmission speed are necessary to obtain such a bound.
We identify proper quantum computation with computational processes that cannot be efficiently simulated on a classical computer. For optical quantum computation, we establish no-go theorems for classes of quantum optical experiments that cannot yield proper quantum computation, and we identify requirements for optical proper quantum computation that correspond to violations of assumptions underpinning the no-go theorems.
We propose a method for classical simulation of finite-dimensional quantum systems, based on sampling from a quasiprobability distribution, i.e., a generalized Wigner function. Our construction applies to all finite dimensions, with the most interesting case being that of qubits. For multiple qubits, we find that quantum computation by Clifford gates and Pauli measurements on magic states can be efficiently classically simulated if the quasiprobability distribution of the magic states is non-negative. This provides the so far missing qubit counterpart of the corresponding result [V. Veitch et al., New J. Phys. 14, 113011 (2012)] applying only to odd dimension. Our approach is more general than previous ones based on mixtures of stabilizer states. Namely, all mixtures of stabilizer states can be efficiently simulated, but for any number of qubits there also exist efficiently simulable states outside the stabilizer polytope. Further, our simulation method extends to negative quasiprobability distributions, where it provides amplitude estimation. The simulation cost is then proportional to a robustness measure squared. For all quantum states, this robustness is smaller than or equal to robustness of magic.
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