Perfect state transfer in quantum spin networks

We propose a class of qubit networks that admit perfect transfer of any quantum state in a fixed period of time. Unlike many other schemes for quantum computation and communication, these networks do not require qubit couplings to be switched on and off. When restricted to N-qubit spin networks of identical qubit couplings, we show that 2 log_3 N is the maximal perfect communication distance for hypercube geometries. Moreover, if one allows fixed but different couplings between the qubits then perfect state transfer can be achieved over arbitrarily long distances in a linear chain.Comment: 4 pages, 1 figur

Finding quantum algorithms via convex optimization

In this paper we describe how to use convex optimization to design quantum algorithms for certain computational tasks. In particular, we consider the ordered search problem, where it is desired to find a specific item in an ordered list of N items. While the best classical algorithm for this problem uses log_2 N queries to the list, a quantum computer can solve this problem much faster. By characterizing a class of quantum query algorithms for ordered search in terms of a semidefinite program, we find quantum algorithms using 4 log_(605) N ≈ 0.433 log_2 N queries, which improves upon the previously best known exact algorithm

Logical Majorana fermions for fault-tolerant quantum simulation

We show how to absorb fermionic quantum simulation's expensive fermion-to-qubit mapping overhead into the overhead already incurred by surface-code-based fault-tolerant quantum computing. The key idea is to process information in surface-code twist defects, which behave like logical Majorana fermions. Our approach implements a universal set of fault-tolerant gates on these logical Majorana fermions by effecting encoded measurement-based topological quantum computing with them. A critical feature of our approach is the use of code deformations between logical tetron and logical hexon surface-code-patch encodings, which enables one to move beyond the limitations of a wholly square-patch tetronic surface-code approach. To motivate near-term implementations, we also show how one could realize each of a universal set of logical Majorana gates on a small-scale testbed using noisy intermediate scale quantum (NISQ) technology on as few as 13 qubits.Comment: 14 pages, 15 figure

Efficient feedback controllers for continuous-time quantum error correction

We present an efficient approach to continuous-time quantum error correction that extends the low-dimensional quantum filtering methodology developed by van Handel and Mabuchi [quant-ph/0511221 (2005)] to include error recovery operations in the form of real-time quantum feedback. We expect this paradigm to be useful for systems in which error recovery operations cannot be applied instantaneously. While we could not find an exact low-dimensional filter that combined both continuous syndrome measurement and a feedback Hamiltonian appropriate for error recovery, we developed an approximate reduced-dimensional model to do so. Simulations of the five-qubit code subjected to the symmetric depolarizing channel suggests that error correction based on our approximate filter performs essentially identically to correction based on an exact quantum dynamical model

Improved quantum algorithms for the ordered search problem via semidefinite programming

One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log_2 N queries to the list, a quantum computer can solve the problem using a constant factor fewer queries. However, the precise value of this constant is unknown. By characterizing a class of quantum query algorithms for ordered search in terms of a semidefinite program, we find new quantum algorithms for small instances of the ordered search problem. Extending these algorithms to arbitrarily large instances using recursion, we show that there is an exact quantum ordered search algorithm using 4 log_{605} N \approx 0.433 log_2 N queries, which improves upon the previously best known exact algorithm.Comment: 8 pages, 4 figure

Perfect Transfer of Arbitrary States in Quantum Spin Networks

We propose a class of qubit networks that admit perfect state transfer of any two-dimensional quantum state in a fixed period of time. We further show that such networks can distribute arbitrary entangled states between two distant parties, and can, by using such systems in parallel, transmit the higher dimensional systems states across the network. Unlike many other schemes for quantum computation and communication, these networks do not require qubit couplings to be switched on and off. When restricted to $N$-qubit spin networks of identical qubit couplings, we show that $2\log_3 N$ is the maximal perfect communication distance for hypercube geometries. Moreover, if one allows fixed but different couplings between the qubits then perfect state transfer can be achieved over arbitrarily long distances in a linear chain. This paper expands and extends the work done in PRL 92, 187902.Comment: 12 pages, 3 figures with updated reference

Quantum search by measurement

We propose a quantum algorithm for solving combinatorial search problems that uses only a sequence of measurements. The algorithm is similar in spirit to quantum computation by adiabatic evolution, in that the goal is to remain in the ground state of a time-varying Hamiltonian. Indeed, we show that the running times of the two algorithms are closely related. We also show how to achieve the quadratic speedup for Grover's unstructured search problem with only two measurements. Finally, we discuss some similarities and differences between the adiabatic and measurement algorithms.Comment: 8 pages, 2 figure