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arXiv:1909.09980 · Physical Review Letters

Complete Quantum-State Tomography with a Local Random Field

Pengcheng Yang, Min Yu, Ralf Betzholz, Christian Arenz, Jianming Cai

Published Jan 10, 2020• 20 citations
arXivHTMLPDF

Abstract

Single-qubit measurements are typically insufficient for inferring arbitrary quantum states of a multiqubit system. We show that, if the system can be fully controlled by driving a single qubit, then utilizing a local random pulse is almost always sufficient for complete quantum-state tomography. Experimental demonstrations of this principle are presented using a nitrogen-vacancy (NV) center in diamond coupled to a nuclear spin, which is not directly accessible. We report the reconstruction of a highly entangled state between the electron and nuclear spin with fidelity above 95% by randomly driving and measuring the NV-center electron spin only. Beyond quantum-state tomography, we outline how this principle can be leveraged to characterize and control quantum processes in cases where the system model is not known.

DOI
10.1103/physrevlett.124.010405

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High fidelity quantum state tomography of electron-14^{14}14N nuclear hybrid spin register in diamond using Rabi oscillations
We report on a new quantum state characterisation method, which we call Rabi-based Quantum State Tomography (RQST), that we have validated on single-qubit quantum states, in particular on the electron and nuclear spins of a single nitrogen-vacancy (NV) centre in diamond, demonstrating high fidelities. The difference of RQST with conventional tomography methods is in the implementation of rotation operators and construction of density matrix from the measured data sets. We demonstrate efficient quantum state control of the electron spin at room temperature with an average fidelity of 0.995 over more than 40 measurements on different states on the Bloch sphere with a maximum fidelity of 0.99992. Also, we apply the methodology to the dark NV nuclear spin state. The state is read via the electron spin using the C-NOT two-qubit entanglement gate and demonstrate fidelities of the same order.
The nitrogen-vacancy (NV) center in diamond is one of the advanced candidates for solid-state quantum computing at room temperature and has proven to be competitive in terms of gate fidelity and the availability of quantum error correction codes. Ambient solid-state qubits may therefore provide quantum computing architectures as an alternative to current solutions. The NV center has an associated electronic spin that is conventionally read out via photoluminescence. As an alternative, the electrical readout is not limited by the confocal resolution of quantum microscopes, which is required in the development of NV-based quantum processors to establish a scalable individual single-spin readout on the order of a few nanometers (necessary for strong dipole-dipole coupling). In this work, the performance of photoelectric readout versus traditional optical readout is investigated to perform Quantum State Tomography measurements on a single NV center. A state fidelity of 0.995 ±\pm± 0.006 is achieved using photoelectrical spin-state readout for state reconstruction, comparable to simultaneous optical measurements. We report photocurrent signal delays, which significantly slow down the photocurrent tomography. We develop a model describing their origin, and propose strategies for their mitigation.
Quantum state tomography is the procedure for reconstructing unknown quantum states from a series of measurements of different observables. Depending on the physical system, different sets of observables have been used for this procedure. In the case of spin qubits, the most common procedure is to measure the transverse magnetization of the system as a function of time. Here, we present a different scheme that relies on time-independent observables and therefore does not require measurements at different evolution times, thereby greatly reducing the overall measurement time. To recover the full density matrix, we use a set of unitary operations that transform the density operator elements into the directly measurable observable. We demonstrate the performance of this scheme in the electron-nuclear spin system of the nitrogen vacancy center in diamond.
We employ a quantum computer to simulate the effect of spin impurities on nitrogen-vacancy (NV) centers in diamond. As these defects operate as nanoscale quantum sensors, modeling quantum noise is crucial to identify limitations in precision. The analysis is performed by means of quantum state tomography on two transmon qubits, representing respectively the NV center and a single spin impurity, modeling either a nuclear spin or an additional NV center. We demonstrate a versatile platform to simulate benchmark protocols such as Ramsey or Hahn-echo. Although we focus on a two-spin system, the same approach opens the door to using quantum processors as scalable simulators of many-spin environments, intractable in classical simulation due to the rapid exponential growth of the Hilbert space. The results reveal the effect different spin-sensor coupling regimes have on coherence, helping to identify detection schemes that maximize the sensitivity under the effect of impurities. Moreover, the role of entanglement generation is analyzed using the Peres-Horodecki criterion and CHSH inequalities. Although no violation of the latter is observed, the presence of entanglement is confirmed.
Long-time dynamical decoupling and quantum control of qubits require high-precision control pulses. Full characterization (quantum tomography) of imperfect pulses presents a bootstrap problem: tomography requires initial states of a qubit which cannot be prepared without perfect pulses. We present a protocol for pulse error analysis, specifically tailored for a wide range of the single solid-state electron spins. Using a single electron spin of a nitrogen-vacancy center in diamond, we experimentally verify the correctness of the protocol, and demonstrate its usefulness for quantum control tasks.