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arXiv:quant-ph/0306143 · Physical Review A

Quantum gate arrays can be programmed to evaluate the expectation value of any operator

Juan Pablo Paz, Augusto J. Roncaglia

Published Nov 21, 2003• 42 citations
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Abstract

A programmable gate array is a circuit whose action is controlled by input data. In this paper we describe a special-purpose quantum circuit that can be programmed to evaluate the expectation value of any operator O acting on a space of states of N dimensions. The circuit has a program register whose state $|\ensuremath{\Psi}(O){〉}_{P}$ encodes the operator O whose expectation value is to be evaluated. The method requires knowledge of the expansion of O in a basis of the space of operators. We discuss some applications of this circuit and its relation to known instances of quantum state tomography.

DOI
10.1103/physreva.68.052316

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A programmable gate array is a circuit whose action is controlled by input data. In this paper we describe a special-purpose quantum circuit that can be programmed to evaluate the expectation value of any operator O acting on a space of states of N dimensions. The circuit has a program register whose state ∣\ensuremathΨ(O)〉P|\ensuremath{\Psi}(O){〉}_{P}∣\ensuremathΨ(O)〉P​ encodes the operator O whose expectation value is to be evaluated. The method requires knowledge of the expansion of O in a basis of the space of operators. We discuss some applications of this circuit and its relation to known instances of quantum state tomography.
We show how to construct quantum gate arrays that can be programmed to perform different unitary operations on a data register, depending on the input to some program register. It is shown that a universal quantum gate array---a gate array which can be programmed to perform any unitary operation---exists only if one allows the gate array to operate in a probabilistic fashion. Thus it is not possible to build a fixed, general purpose quantum computer which can be programmed to perform an arbitrary quantum computation.
We present a probabilistic quantum processor for qubits. The processor itself is represented by a fixed array of gates. The input of the processor is constituted by two registers. In the program register the set of instructions (program) is encoded. This program is applied to the data register. The processor we present can perform any operation on a single qubit with a certain probability. If the operation is unitary, the probability is in general 1/4, but for more restricted sets of operators the probability can be higher.
We present a probabilistic quantum processor for qudits on a single qudit of dimension N. The processor itself is represented by a fixed array of gates. The input of the processor consists of two registers. In the program register the set of instructions (program) is encoded. This program is applied to the data register. The processor can perform any operation on a single qudit of dimension N with a certain probability. For a general unitary operation, the probability is 1/N2,{1/N}^{2},1/N2, but for more restricted sets of operators the probability can be higher. In fact, this probability can be independent of the dimension of the qudit Hilbert space of the qudit under some conditions.
We analyze probabilistic realizations of programmable quantum processors that allow us to realize unitary operations on qubits as well as on qudits. Programmable processors are composed of two inputs — the data register and the program register. In the input state of the program register information about the operation that is supposed to be performed on the data is encoded. At the output of the probabilistic processor a measurement over the program register is performed. An intrinsic property of probabilistic processors is that they sometimes fail, but we know when this happens. We present a complete analysis of two processors: (1) The so-called [Formula: see text] processor that is based on a simple controlled-NOT gate. (2) The so-called [Formula: see text] processor that utilizes the quantum-information-distributor circuit.
We present a photonic integrated circuit architecture for a quantum programmable gate array (QPGA) capable of preparing arbitrary quantum states and operators. The architecture consists of a lattice of phase-modulated Mach-Zehnder interferometers, which perform rotations on path-encoded photonic qubits, and embedded quantum emitters, which use a two-photon scattering process to implement a deterministic controlled-${\ensuremath{\sigma}}_{z}$ operation between adjacent qubits. By appropriately setting phase shifts within the lattice, the device can be programmed to implement any quantum circuit without hardware modifications. We provide algorithms for exactly preparing arbitrary quantum states and operators on the device, and we show that gradient-based optimization can train a simulated QPGA to automatically implement highly compact approximations to important quantum circuits with near-unity fidelity.