Simulating Quantum Systems Using Real Hilbert Spaces

McKague, Matthew; Mosca, Michele; Gisin, Nicolas

doi:10.1103/physrevlett.102.020505

Cited by 72 publications

(93 citation statements)

References 5 publications

(7 reference statements)

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“…So far, the literature has generally focused on the discrete evolution of a quantum system, but recently, continuous evolution has also been discussed McKague et al, 2009). Furthermore, it is usually assumed that there is no restriction in applying one-and two-qubit gates and that all qubits of the simulator can be individually addressed and measured.…”

Section: A Digital Quantum Simulation (Dqs)mentioning

confidence: 99%

Quantum simulation

2014

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Simulating quantum mechanics is known to be a difficult computational problem, especially when dealing with large systems. However, this difficulty may be overcome by using some controllable quantum system to study another less controllable or accessible quantum system, i.e., quantum simulation. Quantum simulation promises to have applications in the study of many problems in, e.g., condensed-matter physics, high-energy physics, atomic physics, quantum chemistry and cosmology. Quantum simulation could be implemented using quantum computers, but also with simpler, analog devices that would require less control, and therefore, would be easier to construct. A number of quantum systems such as neutral atoms, ions, polar molecules, electrons in semiconductors, superconducting circuits, nuclear spins and photons have been proposed as quantum simulators. This review outlines the main theoretical and experimental aspects of quantum simulation and emphasizes some of the challenges and promises of this fast-growing field.

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Section: A Digital Quantum Simulation (Dqs)mentioning

confidence: 99%

Quantum simulation

2014

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“…To deal with issue (i) recall that real gates suffice for universal quantum computation (Bernstein & Vazirani 1997;McKague et al 2009) and given any quantum circuit there is an equivalent circuit comprising real gates from the special orthogonal group that has one extra ancillary rebit line B. This construction is a direct consequence of the algebra isomorphism…”

Section: And the Translation Of Description Will Be Computable In Spamentioning

confidence: 99%

Matchgate and space-bounded quantum computations are equivalent

et al. 2009

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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 characterize their power as coinciding with polynomial-time and logarithmic-space-bounded universal unitary quantum computation.

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“…These observations point to aspects of rqt that cannot be realized within the usual cqm framework. However, the evolution and measurement of a multipartite complex quantum state under discrete or continuous evolution in cqm can be simulated using states and operators in rqt [7].…”

Section: Introductionmentioning

confidence: 99%

Quaternionic Quantum Dynamics on Complex Hilbert Spaces

Graydon

2013

Found Phys

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We consider a quaternionic quantum formalism for the description of quantum states and quantum dynamics. We prove that generalized quantum measurements on physical systems in quaternionic quantum theory can be simulated by usual quantum measurements with positive operator valued measures on complex Hilbert spaces. Furthermore, we prove that quaternionic quantum channels can be simulated by completely positive trace preserving maps on complex matrices. These novel results map all quaternionic quantum processes to algorithms in usual quantum information theory.

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Simulating Quantum Systems Using Real Hilbert Spaces

Cited by 72 publications

References 5 publications

Quantum simulation

Quantum simulation

Matchgate and space-bounded quantum computations are equivalent

Quaternionic Quantum Dynamics on Complex Hilbert Spaces

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