Quantum simulations under translational symmetry

Kraus, Christina V.; Wolf, Michael M.; Cirac, J. I.

doi:10.1103/physreva.75.022303

Cited by 19 publications

(35 citation statements)

References 33 publications

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“…More precisely, the question whether (and to which extent) one quantum system can simulate another one can be answered by analysing the Lie-subalgebra structure of systems with a given dimension. Recently Kraus et al have explored whether target quantum systems can be universally simulated on translationally invariant lattices of bosonic, fermionic, and spin systems [17]. Based on the branching diagrams of simple subalgebras to su(N ), here we take a more general approach pursuing the question which type of quantum system can simulate a given one with least overhead in state-space dimension.…”

Section: Simulabilitymentioning

confidence: 99%

“…For the p-th level of the system, f † p and f p change the occupation numbers n p labelling the respective states |n p such as to give f † p |0 = |1 = ( 1 0 ) = |↑ and f p |1 = |0 = ( 0 1 ) = |↓ , where by the Pauli principle n p ∈ {0, 1}, (f † p ) 2 ≡ 0, and (f p ) 2 ≡ 0. Now the properties of the usual quadratic Hamiltonians (see, e.g., [112,113,114,17,115])…”

Section: Fermionic Quantum Systemsmentioning

confidence: 99%

“…so(128) so(16) so(9) so(15) su(256)sp(128) su(2)sp(2)so(256) so(17) su(4)so(18) su(512) sp(256) su(2) so(20) so(19) so(512) su(3) so(7)sp(3)su(1024)sp(512)su(2)so(21)sp(2)so(1024) su(5)so(22)su(2048)sp(1024)su(2)so(2048) so(24)so(23)su(4096)sp(2048)su(2)sp(2)so(4096)su(3)so(7)so(17)so(25) sp(4)so(6)so(8)f 4 g 2 so(26)su(8192)sp(4096)su(2)so(28) so(27) so(8192)su(16384)sp(8192)su(2)so(29) sp(2)so(16384)su(4)so(30) su(32768)sp(16384)su(2)su(6)so(32768)su(3)sp(3)so(8)so(32) so(31) …”

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confidence: 99%

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Symmetry principles in quantum systems theory

Zeier

Schulte-Herbrueggen

2011

Journal of Mathematical Physics

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General dynamic properties like controllability and simulability of spin systems, fermionic and bosonic systems are investigated in terms of symmetry. Symmetries may be due to the interaction topology or due to the structure and representation of the system and control Hamiltonians. In either case, they obviously entail constants of motion. Conversely, the absence of symmetry implies irreducibility and provides a convenient necessary condition for full controllability much easier to assess than the well-established Lie-algebra rank condition. We give a complete lattice of irreducible simple subalgebras of su(2 n ) for up to n = 15 qubits. It complements the symmetry condition by allowing for easy tests solving homogeneous linear equations to filter irreducible unitary representations of other candidate algebras of classical type as well as of exceptional types. -The lattice of irreducible simple subalgebras given also determines mutual simulability of dynamic systems of spin or fermionic or bosonic nature. We illustrate how controlled quadratic fermionic (and bosonic) systems can be simulated by spin systems and in certain cases also vice versa.

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Section: Simulabilitymentioning

confidence: 99%

Section: Fermionic Quantum Systemsmentioning

confidence: 99%

mentioning

confidence: 99%

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Symmetry principles in quantum systems theory

Zeier

Schulte-Herbrueggen

2011

Journal of Mathematical Physics

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“…An interesting question is what Hamiltonians can be simulated under certain control constraints. For example, (Kraus et al, 2007) discussed the class of Hamiltonians that can be simulated when one is restricted to applying translationally invariant Hamiltonians. The authors showed that if both local and nearest-neighbor interactions are controllable, then the simulation of interactions in quadratic fermionic and bosonic systems is possible.…”

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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“…An alternative approach is to avoid addressing individual atoms altogether. Kraus et al [71] explore the potential of simulations using only global single-particle and nearest neighbor interactions. This is a good approximation for atoms in optical lattices, and the three types of subsystem they considerfermions, bosons, and spins -can be realised by choosing different atoms to trap in the optical lattice and tuning the lattice parameters to different regimes.…”

Section: Atom Trap and Ion Trap Architecturesmentioning

confidence: 99%

Using Quantum Computers for Quantum Simulation

Brown

Munro

Kendon

2010

Entropy

128

101

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Numerical simulation of quantum systems is crucial to further our understanding of natural phenomena. Many systems of key interest and importance, in areas such as superconducting materials and quantum chemistry, are thought to be described by models which we cannot solve with sufficient accuracy, neither analytically nor numerically with classical computers. Using a quantum computer to simulate such quantum systems has been viewed as a key application of quantum computation from the very beginning of the field in the 1980s. Moreover, useful results beyond the reach of classical computation are expected to be accessible with fewer than a hundred qubits, making quantum simulation potentially one of the earliest practical applications of quantum computers. In this paper we survey the theoretical and experimental development of quantum simulation using quantum computers, from the first ideas to the intense research efforts currently underway.

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Quantum simulations under translational symmetry

Cited by 19 publications

References 33 publications

Symmetry principles in quantum systems theory

Symmetry principles in quantum systems theory

Quantum simulation

Using Quantum Computers for Quantum Simulation

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