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arXiv:quant-ph/0603248 · Physical Review Letters

Benchmarking Quantum Control Methods on a 12-Qubit System

C. Negrevergne, T. S. Mahesh, Colm A. Ryan, Michael J. T. Ditty, Francis-Yan Cyr-Racine, William P. Power, Nicolas Boulant, Timothy F. Havel, David G. Cory, Raymond Laflamme

Published May 1, 2006• 200 citations
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Abstract

In this Letter, we present an experimental benchmark of operational control methods in quantum information processors extended up to 12 qubits. We implement universal control of this large Hilbert space using two complementary approaches and discuss their accuracy and scalability. Despite decoherence, we were able to reach a 12-coherence state (or a 12-qubit pseudopure cat state) and decode it into an 11 qubit plus one qutrit pseudopure state using liquid state nuclear magnetic resonance quantum information processors.

DOI
10.1103/physrevlett.96.170501

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In this Letter, we present an experimental benchmark of operational control methods in quantum information processors extended up to 12 qubits. We implement universal control of this large Hilbert space using two complementary approaches and discuss their accuracy and scalability. Despite decoherence, we were able to reach a 12-coherence state (or a 12-qubit pseudopure cat state) and decode it into an 11 qubit plus one qutrit pseudopure state using liquid state nuclear magnetic resonance quantum information processors.
In building a quantum-information processor (QIP), the challenge is to coherently control a large quantum system well enough to perform an arbitrary quantum algorithm and to be able to correct errors induced by decoherence. Nuclear magnetic resonance (NMR) QIPs offer an excellent testbed on which to develop and benchmark tools and techniques to control quantum systems. Two main issues to consider when designing control methods are accuracy and efficiency, for which two complementary approaches have been developed so far to control qubit registers with liquid-state NMR methods. The first applies optimal control theory to numerically optimize the control fields to implement unitary operations on low-dimensional systems with high fidelity. The second technique is based on the efficient optimization of a sequence of imperfect control elements so that implementation of a full quantum algorithm is possible while minimizing error accumulation. This paper summarizes our work in implementing both of these methods. Furthermore, we show that taken together, they form a basis to design quantum control methods for a block-architecture QIP so that large system size is not a barrier to implementing optimal control techniques.
We propose and experimentally realize an algorithmic benchmark that demonstrates coherent control with a sequence of quantum operations that first generates and then decodes the cat state (|000...>+|111...>)/sqrt(2) to the standard initial state |000...>. This is the first high fidelity experimental quantum algorithm on the currently largest physical quantum register, which has seven quantum bits (qubits) provided by the nuclei of crotonic acid. The experiment has the additional benefit of verifying a seven coherence in a generic system of coupled spins. Our implementation combines numerous nuclear magnetic resonance (NMR) techniques in one experiment and introduces practical methods for translating quantum networks to control operations. The experimental procedure can be used as a reliable and efficient method for creating a standard pseudo-pure state, the first step for implementing traditional quantum algorithms in liquid state NMR. The benchmark and the techniques can be adapted for use on other proposed quantum devices.
Being able to quantify the level of coherent control in a proposed device implementing a quantum information processor (QIP) is an important task for both comparing different devices and assessing a device's prospects with regards to achieving fault-tolerant quantum control. We implement in a liquid-state nuclear magnetic resonance QIP the randomized benchmarking protocol presented by Knill et al (2008 Phys. Rev. A 77 012307). We report an error per randomized π/2 pulse of 1.3±0.1 × 10 −4 with a single-qubit QIP and show an experimentally relevant error model where the randomized benchmarking gives a signature fidelity decay which is not possible to interpret as a single error per gate. We explore and experimentally investigate multi-qubit extensions of this protocol and report an average error rate for one- and two-qubit gates of 4.7±0.3 × 10 −3 for a three-qubit QIP. We estimate that these error rates are still not decoherence limited and thus can be improved with modifications to the control hardware and software.
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We demonstrate the implementation of an entanglement swapping operation on a four-qubit liquid-state nuclear-magnetic-resonance (NMR) quantum-information processor. We use this experiment as a benchmark to illustrate the progress made in the field of quantum control using strongly modulating pulses and a correction scheme for removing distortions introduced by the nonlinearities in the transmitter and probe circuits. The advances include compensating for incoherent errors caused by the spatial variation of the system Hamiltonian in the NMR sample. The goal of these control sequences is to cause the collapse of the Kraus operator-sum representation of the superoperator into one unitary operator so that the ensemble appears to evolve as one coherent whole.
Theoretical Quantum Information Processing (QIP) has matured from the use of qubits to the use of qudits (systems having states >2). Whereas most of the experimental implementations have been performed using qubits, little experimental work has been carried out using qudits as yet. In this paper we demonstrate experimental realization of a qutrit system by nuclear magnetic resonance (NMR), utilizing deuterium (spin-1) nuclei partially oriented in liquid crystalline phase. Preparation of pseudopure states and implementation of unitary operations are demonstrated in this single-qutrit system, using transition selective pulses.