Protecting information via probabilistic cellular automata.

Probabilistic cellular automata describe the dynamics of classical spin models, which, for sufficiently small temperature T, can serve as classical memory capable of storing information even in the presence of nonzero external magnetic field h. In this article, we study a recently introduced probabilistic cellular automaton, the sweep rule, and map out a region of two coexisting stable phases in the (T,h) plane. We also find that the sweep rule belongs to the weak two-dimensional Ising universality class. Our work is a step towards understanding how simple geometrically local error-correction strategies can protect information encoded into complex noisy systems, such as topological quantum error-correcting codes.

Experimental Activation of Strong Local Passive States with Quantum Information.

Strong local passivity is a property of multipartite quantum systems from which it is impossible to extract energy locally. Surprisingly, if the strong local passive state displays entanglement, it could be possible to locally activate energy density by adding classical communication between different partitions of the system, through so-called "quantum energy teleportation" protocols. Here, we report both the first experimental observation of local activation of energy density on an entangled state and the first realization of a quantum energy teleportation protocol using nuclear magnetic resonance on a bipartite quantum system.

Hybrid quantum-classical approach to enhanced quantum metrology.

Quantum metrology plays a fundamental role in many scientific areas. However, the complexity of engineering entangled probes and the external noise raise technological barriers for realizing the expected precision of the to-be-estimated parameter with given resources. Here, we address this problem by introducing adjustable controls into the encoding process and then utilizing a hybrid quantum-classical approach to automatically optimize the controls online. Our scheme does not require any complex or intractable off-line design, and it can inherently correct certain unitary errors during the learning procedure. We also report the first experimental demonstration of this promising scheme for the task of finding optimal probes for frequency estimation on a nuclear magnetic resonance (NMR) processor. The proposed scheme paves the way to experimentally auto-search optimal protocol for improving the metrology precision.

Experimental Implementation of Efficient Quantum Pseudorandomness on a 12-Spin System.

Quantum pseudorandomness, also known as unitary designs, comprises a powerful resource for emergent quantum technologies. Although in theory pseudorandom unitary operators can be constructed efficiently, realizing these objects in realistic physical systems is a challenging task. Here, we demonstrate experimental generation and detection of quantum pseudorandomness on a 12-qubit nuclear magnetic resonance system. We first apply random sequences to the interacting nuclear spins, leading to random quantum evolutions that can quickly form unitary designs. Then, in order to probe the growth of quantum pseudorandomness during the time evolutions, we propose the idea of using the system's multiple-quantum coherence distribution as an indicator. Based on this indicator, we measure the spreading of quantum coherences and find that substantial quantum pseudorandomness has been achieved at the 12-qubit scale. This may open up a path to experimentally explore quantum randomness on forthcoming large-scale quantum processors.

Quantum Error Correction Decoheres Noise.

Typical studies of quantum error correction assume probabilistic Pauli noise, largely because it is relatively easy to analyze and simulate. Consequently, the effective logical noise due to physically realistic coherent errors is relatively unknown. Here, we prove that encoding a system in a stabilizer code and measuring error syndromes decoheres errors, that is, causes coherent errors to converge toward probabilistic Pauli errors, even when no recovery operations are applied. Two practical consequences are that the error rate in a logical circuit is well quantified by the average gate fidelity at the logical level and that essentially optimal recovery operators can be determined by independently optimizing the logical fidelity of the effective noise per syndrome.

Correlation-Enhanced Algorithmic Cooling.

We propose a method for increasing the purity of interacting quantum systems that takes advantage of correlations present due to the internal interaction. In particular, when this interaction is sufficiently strong, we show that by using the system's quantum correlations one can achieve cooling beyond established limits of previous conventional algorithmic cooling proposals which assume no interaction.

Experimental Identification of Non-Abelian Topological Orders on a Quantum Simulator.

Topological orders can be used as media for topological quantum computing-a promising quantum computation model due to its invulnerability against local errors. Conversely, a quantum simulator, often regarded as a quantum computing device for special purposes, also offers a way of characterizing topological orders. Here, we show how to identify distinct topological orders via measuring their modular S and T matrices. In particular, we employ a nuclear magnetic resonance quantum simulator to study the properties of three topologically ordered matter phases described by the string-net model with two string types, including the Z_{2} toric code, doubled semion, and doubled Fibonacci. The third one, non-Abelian Fibonacci order is notably expected to be the simplest candidate for universal topological quantum computing. Our experiment serves as the basic module, built on which one can simulate braiding of non-Abelian anyons and ultimately, topological quantum computation via the braiding, and thus provides a new approach of investigating topological orders using quantum computers.

Quantum State Tomography via Reduced Density Matrices.

Quantum state tomography via local measurements is an efficient tool for characterizing quantum states. However, it requires that the original global state be uniquely determined (UD) by its local reduced density matrices (RDMs). In this work, we demonstrate for the first time a class of states that are UD by their RDMs under the assumption that the global state is pure, but fail to be UD in the absence of that assumption. This discovery allows us to classify quantum states according to their UD properties, with the requirement that each class be treated distinctly in the practice of simplifying quantum state tomography. Additionally, we experimentally test the feasibility and stability of performing quantum state tomography via the measurement of local RDMs for each class. These theoretical and experimental results demonstrate the advantages and possible pitfalls of quantum state tomography with local measurements.

Thresholds for Universal Concatenated Quantum Codes.

Quantum error correction and fault tolerance make it possible to perform quantum computations in the presence of imprecision and imperfections of realistic devices. An important question is to find the noise rate at which errors can be arbitrarily suppressed. By concatenating the 7-qubit Steane and 15-qubit Reed-Muller codes, the 105-qubit code enables a universal set of fault-tolerant gates despite not all of them being transversal. Importantly, the cnot gate remains transversal in both codes, and as such has increased error protection relative to the other single qubit logical gates. We show that while the level-1 pseudothreshold for the concatenated scheme is limited by the logical Hadamard gate, the error suppression of the logical cnot gates allows for the asymptotic threshold to increase by orders of magnitude at higher levels. We establish a lower bound of 1.28×10^{-3} for the asymptotic threshold of this code, which is competitive with known concatenated models and does not rely on ancillary magic state preparation for universal computation.

Tomography is Necessary for Universal Entanglement Detection with Single-Copy Observables.

Entanglement, one of the central mysteries of quantum mechanics, plays an essential role in numerous tasks of quantum information science. A natural question of both theoretical and experimental importance is whether universal entanglement detection can be accomplished without full state tomography. In this Letter, we prove a no-go theorem that rules out this possibility for nonadaptive schemes that employ single-copy measurements only. We also examine a previously implemented experiment [H. Park et al., Phys. Rev. Lett. 105, 230404 (2010)], which claimed to detect entanglement of two-qubit states via adaptive single-copy measurements without full state tomography. In contrast, our simulation and experiment both support the opposite conclusion that the protocol, indeed, leads to full state tomography, which supplements our no-go theorem. These results reveal a fundamental limit of single-copy measurements in entanglement detection and provide a general framework of the detection of other interesting properties of quantum states, such as the positivity of partial transpose and the k-symmetric extendibility.

Randomized benchmarking of quantum gates implemented by electron spin resonance.

Spin systems controlled and probed by magnetic resonance have been valuable for testing the ideas of quantum control and quantum error correction. This paper introduces an X-band pulsed electron spin resonance spectrometer designed for high-fidelity coherent control of electron spins, including a loop-gap resonator for sub-millimeter sized samples with a control bandwidth ∼40MHz. Universal control is achieved by a single-sideband upconversion technique with an I-Q modulator and a 1.2GS/s arbitrary waveform generator. A single qubit randomized benchmarking protocol quantifies the average errors of Clifford gates implemented by simple Gaussian pulses, using a sample of gamma-irradiated quartz. Improvements in unitary gate fidelity are achieved through phase transient correction and hardware optimization. A preparation pulse sequence that selects spin packets in a narrowed distribution of static fields confirms that inhomogeneous dephasing (1/T2(∗)) is the dominant source of gate error. The best average fidelity over the Clifford gates obtained here is 99.2%, which serves as a benchmark to compare with other technologies.

Achievable Polarization for Heat-Bath Algorithmic Cooling.

Pure quantum states play a central role in applications of quantum information, both as initial states for quantum algorithms and as resources for quantum error correction. Preparation of highly pure states that satisfy the threshold for quantum error correction remains a challenge, not only for ensemble implementations like NMR or ESR but also for other technologies. Heat-bath algorithmic cooling is a method to increase the purity of a set of qubits coupled to a bath. We investigated the achievable polarization by analyzing the limit when no more entropy can be extracted from the system. In particular, we give an analytic form for the maximum polarization achievable for the case when the initial state of the qubits is totally mixed, and the corresponding steady state of the whole system. It is, however, possible to reach higher polarization while starting with certain states; thus, our result provides an achievable bound. We also give the number of steps needed to get a specific required polarization.

Estimating the Coherence of Noise in Quantum Control of a Solid-State Qubit.

To exploit a given physical system for quantum information processing, it is critical to understand the different types of noise affecting quantum control. Distinguishing coherent and incoherent errors is extremely useful as they can be reduced in different ways. Coherent errors are generally easier to reduce at the hardware level, e.g., by improving calibration, whereas some sources of incoherent errors, e.g., T_{2}^{*} processes, can be reduced by engineering robust pulses. In this work, we illustrate how purity benchmarking and randomized benchmarking can be used together to distinguish between coherent and incoherent errors and to quantify the reduction in both of them due to using optimal control pulses and accounting for the transfer function in an electron spin resonance system. We also prove that purity benchmarking provides bounds on the optimal fidelity and diamond norm that can be achieved by correcting the coherent errors through improving calibration.

Experimental estimation of average fidelity of a Clifford gate on a 7-qubit quantum processor.

One of the major experimental achievements in the past decades is the ability to control quantum systems to high levels of precision. To quantify the level of control we need to characterize the dynamical evolution. Full characterization via quantum process tomography is impractical and often unnecessary. For most practical purposes, it is enough to estimate more general quantities such as the average fidelity. Here we use a unitary 2-design and twirling protocol for efficiently estimating the average fidelity of Clifford gates, to certify a 7-qubit entangling gate in a nuclear magnetic resonance quantum processor. Compared with more than 10^{8} experiments required by full process tomography, we conducted 1656 experiments to satisfy a statistical confidence level of 99%. The average fidelity of this Clifford gate in experiment is 55.1%, and rises to at least 87.5% if the signal's decay due to decoherence is taken into account. The entire protocol of certifying Clifford gates is efficient and scalable, and can easily be extended to any general quantum information processor with minor modifications.

Using concatenated quantum codes for universal fault-tolerant quantum gates.

We propose a method for universal fault-tolerant quantum computation using concatenated quantum error correcting codes. The concatenation scheme exploits the transversal properties of two different codes, combining them to provide a means to protect against low-weight arbitrary errors. We give the required properties of the error correcting codes to ensure universal fault tolerance and discuss a particular example using the 7-qubit Steane and 15-qubit Reed-Muller codes. Namely, other than computational basis state preparation as required by the DiVincenzo criteria, our scheme requires no special ancillary state preparation to achieve universality, as opposed to schemes such as magic state distillation. We believe that optimizing the codes used in such a scheme could provide a useful alternative to state distillation schemes that exhibit high overhead costs.

Private quantum subsystems.

We investigate the most general notion of a private quantum code, which involves the encoding of qubits into quantum subsystems and subspaces. We contribute to the structure theory for private quantum codes by deriving testable conditions for private quantum subsystems in terms of Kraus operators for channels, establishing an analogue of the Knill-Laflamme conditions in this setting. For a large class of naturally arising quantum channels, we show that private subsystems can exist even in the absence of private subspaces. In doing so, we also discover the first examples of private subsystems that are not complemented by operator quantum error correcting codes, implying that the complementarity of private codes and quantum error correcting codes fails for the general notion of private quantum subsystems.

Recent advances in nuclear magnetic resonance quantum information processing.

Quantum information processors have the potential to drastically change the way we communicate and process information. Nuclear magnetic resonance (NMR) has been one of the first experimental implementations of quantum information processing (QIP) and continues to be an excellent testbed to develop new QIP techniques. We review the recent progress made in NMR QIP, focusing on decoupling, pulse engineering and indirect nuclear control. These advances have enhanced the capabilities of NMR QIP, and have useful applications in both traditional NMR and other QIP architectures.

Experimental implementation of encoded logical qubit operations in a perfect quantum error correcting code.

Large-scale universal quantum computing requires the implementation of quantum error correction (QEC). While the implementation of QEC has already been demonstrated for quantum memories, reliable quantum computing requires also the application of nontrivial logical gate operations to the encoded qubits. Here, we present examples of such operations by implementing, in addition to the identity operation, the NOT and the Hadamard gate to a logical qubit encoded in a five qubit system that allows correction of arbitrary single-qubit errors. We perform quantum process tomography of the encoded gate operations, demonstrate the successful correction of all possible single-qubit errors, and measure the fidelity of the encoded logical gate operations.

Practical experimental certification of computational quantum gates using a twirling procedure.

Because of the technical difficulty of building large quantum computers, it is important to be able to estimate how faithful a given implementation is to an ideal quantum computer. The common approach of completely characterizing the computation process via quantum process tomography requires an exponential amount of resources, and thus is not practical even for relatively small devices. We solve this problem by demonstrating that twirling experiments previously used to characterize the average fidelity of quantum memories efficiently can be easily adapted to estimate the average fidelity of the experimental implementation of important quantum computation processes, such as unitaries in the Clifford group, in a practical and efficient manner with applicability in current quantum devices. Using this procedure, we demonstrate state-of-the-art coherent control of an ensemble of magnetic moments of nuclear spins in a single crystal solid by implementing the encoding operation for a 3-qubit code with only a 1% degradation in average fidelity discounting preparation and measurement errors. We also highlight one of the advances that was instrumental in achieving such high fidelity control.

Digital quantum simulation of the statistical mechanics of a frustrated magnet.

Many problems of interest in physics, chemistry and computer science are equivalent to problems defined on systems of interacting spins. However, most such problems require computational resources that are out of reach with classical computers. A promising solution to overcome this challenge is quantum simulation. Several 'analogue' quantum simulations of interacting spin systems have been realized experimentally, where ground states were prepared using adiabatic techniques. Here we report a 'digital' quantum simulation of thermal states; a three-spin frustrated magnet was simulated using a nuclear magnetic resonance quantum information processor, and we were able to explore the phase diagram of the system at any simulated temperature and external field. These results help to identify the challenges for performing quantum simulations of physical systems at finite temperatures, and suggest methods that may be useful in simulating thermal open quantum systems.