A polynomial-time algorithm for the ground state of 1D gapped local
... Computing ground states of local Hamiltonians is a fundamental problem in condensed matter physics and is the quantum analog of constraint satisfaction problems. The problem is known to be QMA-complete, even for one-dimensional Hamiltonians [1]. This means that we do not even expect that there is a ...
... Computing ground states of local Hamiltonians is a fundamental problem in condensed matter physics and is the quantum analog of constraint satisfaction problems. The problem is known to be QMA-complete, even for one-dimensional Hamiltonians [1]. This means that we do not even expect that there is a ...
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... On the other hand, a von Neumann algebra A inherits a unital subalgebra from L(H), and according to the first condition in its definition A does indeed inherit a *-subalgebra structure, as further explained in the next section on C*-algebras. Furthermore, we have notable Bicommutant Theorem which st ...
... On the other hand, a von Neumann algebra A inherits a unital subalgebra from L(H), and according to the first condition in its definition A does indeed inherit a *-subalgebra structure, as further explained in the next section on C*-algebras. Furthermore, we have notable Bicommutant Theorem which st ...
Quantum Computing Lecture 1 What is Quantum Computing?
... If we measure the first qubit in the first case, we see |0i with probability 1 and the state remains unchanged. In the second case (an EPR pair), measuring the first bit gives |0i or |1i with equal probability. After this, the second qubit is also ...
... If we measure the first qubit in the first case, we see |0i with probability 1 and the state remains unchanged. In the second case (an EPR pair), measuring the first bit gives |0i or |1i with equal probability. After this, the second qubit is also ...
A Gentle Introduction to Quantum Computing
... computer can1 . For instance numbers can be factored in polynomial time by quantum computers, compared to the exponential time of classical ones. This has brought about a fundamental revolution in the field of complexity theory and cryptography, among others. The problem, however, is that no large ...
... computer can1 . For instance numbers can be factored in polynomial time by quantum computers, compared to the exponential time of classical ones. This has brought about a fundamental revolution in the field of complexity theory and cryptography, among others. The problem, however, is that no large ...
Numerical Renormalization Group methods with Matrix Product States
... What are the questions we would like to see answered? – Ground state properties, energy spectrum, correlation length, criticality, connection between those and entanglement – Are such systems useful, i.e. do they exhibit the right kind of entanglement and allow for the right kind of control, for bui ...
... What are the questions we would like to see answered? – Ground state properties, energy spectrum, correlation length, criticality, connection between those and entanglement – Are such systems useful, i.e. do they exhibit the right kind of entanglement and allow for the right kind of control, for bui ...
Fault-tolerant quantum computation
... qubit is stored nonlocally, shared by many physical qubits, and can be protected if the noise is sufficiently weak and also sufficiently weakly correlated in space and time. Two central questions are: 1) For what noise models does fault-tolerant quantum computing work effectively? 2) For a given noi ...
... qubit is stored nonlocally, shared by many physical qubits, and can be protected if the noise is sufficiently weak and also sufficiently weakly correlated in space and time. Two central questions are: 1) For what noise models does fault-tolerant quantum computing work effectively? 2) For a given noi ...
Testing the Dimension of Hilbert Spaces
... Both of these examples involved three-outcome measurements; so the number of measurement outcomes exceeded the dimension of the Hilbert space to be witnessed. This shows, as one may expect, that not all d-outcome correlations can be obtained by measuring quantum systems of dimension smaller than d. ...
... Both of these examples involved three-outcome measurements; so the number of measurement outcomes exceeded the dimension of the Hilbert space to be witnessed. This shows, as one may expect, that not all d-outcome correlations can be obtained by measuring quantum systems of dimension smaller than d. ...
Universal quantum control in two-electron spin quantum bits using
... all electrical and potentially fast enough to enable 104 gate operations within the coherence time (essential for quantum error correction). The phase space of the two-level system is on a one-to-one correspondence with the points on the surface of a three dimensional sphere, the Bloch sphere2 , whe ...
... all electrical and potentially fast enough to enable 104 gate operations within the coherence time (essential for quantum error correction). The phase space of the two-level system is on a one-to-one correspondence with the points on the surface of a three dimensional sphere, the Bloch sphere2 , whe ...
Simulating large quantum circuits on a small quantum computer
... UCSB and Google are building a 50 qubit quantum computer. They recently simulated random 42-qubit circuits on a supercomputer [BIS+ 16]. ...
... UCSB and Google are building a 50 qubit quantum computer. They recently simulated random 42-qubit circuits on a supercomputer [BIS+ 16]. ...
Dissipated work and fluctuation relations in driven
... Quantum FRs have been discussed till now essentially only for closed systems (Campisi et al., RMP 2011) ...
... Quantum FRs have been discussed till now essentially only for closed systems (Campisi et al., RMP 2011) ...
quantum cryptography - 123SeminarsOnly.com
... consumption lasers in compact disc players. A particularly exciting application of quantum mechanics which is still currently in the theoretical stage is that of quantum computing. Conventional computers use binary digits (bits) set to either one or zero to perform calculations. Quantum computers, i ...
... consumption lasers in compact disc players. A particularly exciting application of quantum mechanics which is still currently in the theoretical stage is that of quantum computing. Conventional computers use binary digits (bits) set to either one or zero to perform calculations. Quantum computers, i ...
Quantum Computing Lecture 1 Bits and Qubits What is Quantum
... Postulate 1: A closed system is described by a unit vector in a complex inner product space. Postulate 2: The evolution of a closed system in a fixed time interval is described by a unitary transform. Postulate 3: If we measure the state |ψi of a system in an orthonormal basis |0i · · · |n − 1i, we ...
... Postulate 1: A closed system is described by a unit vector in a complex inner product space. Postulate 2: The evolution of a closed system in a fixed time interval is described by a unitary transform. Postulate 3: If we measure the state |ψi of a system in an orthonormal basis |0i · · · |n − 1i, we ...
Quantum computing
Quantum computing studies theoretical computation systems (quantum computers) that make direct use of quantum-mechanical phenomena, such as superposition and entanglement, to perform operations on data. Quantum computers are different from digital computers based on transistors. Whereas digital computers require data to be encoded into binary digits (bits), each of which is always in one of two definite states (0 or 1), quantum computation uses quantum bits (qubits), which can be in superpositions of states. A quantum Turing machine is a theoretical model of such a computer, and is also known as the universal quantum computer. Quantum computers share theoretical similarities with non-deterministic and probabilistic computers. The field of quantum computing was initiated by the work of Yuri Manin in 1980, Richard Feynman in 1982, and David Deutsch in 1985. A quantum computer with spins as quantum bits was also formulated for use as a quantum space–time in 1968.As of 2015, the development of actual quantum computers is still in its infancy, but experiments have been carried out in which quantum computational operations were executed on a very small number of quantum bits. Both practical and theoretical research continues, and many national governments and military agencies are funding quantum computing research in an effort to develop quantum computers for civilian, business, trade, and national security purposes, such as cryptanalysis.Large-scale quantum computers will be able to solve certain problems much more quickly than any classical computers that use even the best currently known algorithms, like integer factorization using Shor's algorithm or the simulation of quantum many-body systems. There exist quantum algorithms, such as Simon's algorithm, that run faster than any possible probabilistic classical algorithm.Given sufficient computational resources, however, a classical computer could be made to simulate any quantum algorithm, as quantum computation does not violate the Church–Turing thesis.