The purpose of the research: to determine an efficient and error-resilient method for assessing the fidelity of singlequbit quantum operations, as well as to formulate and experimentally implement an algorithm for determining the average accuracy of single-qubit quantum transformations Research methods: the theory of noisy quantum operations, randomization of single-qubit quantum circuits composed of Clifford group transformations, the theory of unitary 2-design, experimental validation on a quantum computer based on ytterbium-171 trapped ions Research results: an algorithm for estimating the average fidelity of single-qubit operations and its statistical error is described; experimental validation confirmed the correctness of the exponential decay model of the probability of obtaining the target state during measurement as the depth of the quantum circuit increases; the resulting experimental average fidelity of the single-qubit quantum operation is 99.94% Scientific novelty: the application of the randomized benchmarking method to determine the average fidelity of singlequbit quantum operations in quantum computing, particularly for an ion-based quantum processor with ytterbium-171 ions.
The purpose of the research: to determine an efficient and error-resilient method for assessing the fidelity of singlequbit quantum operations, as well as to formulate and experimentally implement an algorithm for determining the average accuracy of single-qubit quantum transformations Research methods: the theory of noisy quantum operations, randomization of single-qubit quantum circuits composed of Clifford group transformations, the theory of unitary 2-design, experimental validation on a quantum computer based on ytterbium-171 trapped ions Research results: an algorithm for estimating the average fidelity of single-qubit operations and its statistical error is described; experimental validation confirmed the correctness of the exponential decay model of the probability of obtaining the target state during measurement as the depth of the quantum circuit increases; the resulting experimental average fidelity of the single-qubit quantum operation is 99.94% Scientific novelty: the application of the randomized benchmarking method to determine the average fidelity of singlequbit quantum operations in quantum computing, particularly for an ion-based quantum processor with ytterbium-171 ions.
Randomised benchmarking is a widely used experimental technique to characterise the average error of quantum operations. Benchmarking procedures that scale to enable the characterisation of n-qubit circuits rely on efficient procedures for manipulating those circuits and, as such, have been limited to subgroups of the Clifford group. However, universal quantum computers require additional, non-Clifford gates to approximate arbitrary unitary transformations. We define a scalable randomised benchmarking procedure over n-qubit unitary matrices that correspond to protected non-Clifford gates for a class of stabiliser codes. We present efficient methods for representing and composing group elements, sampling them uniformly and synthesising corresponding poly(n)-sized circuits. The procedure provides experimental access to two independent parameters that together characterise the average gate fidelity of a group element. A scalable procedure to determine the error of quantum operations has been developed by researchers in the United States. Andrew Cross and colleagues at the IBM T.J. Watson Research Center have expanded previously used protocols to a broader range of quantum circuits, thereby enabling error benchmarking for all common logical operations used in leading quantum computing protocols. The standard technique for error characterization in these devices is randomized benchmarking, which provides benefits such as insensitivity to measurement errors, but on the other hand only functions in a limited number of circumstances. In their theoretical study, the researchers demonstrate how randomized benchmarking approaches can be expanded to a much broader range of logical operations. The procedure can be readily implemented experimentally, and provides access to important experimental noise parameters in quantum computing.
Randomized benchmarking (RB) protocols have become an essential tool for providing a meaningful partial characterization of experimental quantum operations. While the RB decay rate is known to enable estimates of the average fidelity of those operations under gate-independent Markovian noise, under gate-dependent noise this rate is more difficult to interpret rigorously. In this paper, we prove that single-qubit RB decay parameter p coincides with the decay parameter of the gate-set circuit fidelity , a novel figure of merit which characterizes the expected average fidelity over arbitrary circuits of operations from the gate-set. We also prove that, in the limit of high-fidelity single-qubit experiments, the possible alarming disconnect between the average gate fidelity and RB experimental results is simply explained by a basis mismatch between the gates and the state-preparation and measurement procedures, that is, to a unitary degree of freedom in labeling the Pauli matrices. Based on numerical evidence and physically motivated arguments, we conjecture that these results also hold for higher dimensions.
Randomized benchmarking comprises a suite of standard techniques for assessing the operational fidelity of quantum processors. These techniques can be reliably applied to groups with process matrix representations that are free of multiplicity. However, many groups that are naturally formed from native gates do have multiplicity, and it is difficult to draw robust conclusions from the resulting data. In this work, we present a new and intrinsic solution to the problem of multiplicity that completely eliminates the need to fit multi-exponential decays while still remaining robust to errors in state preparation and measurement. Our procedure, which we call lifted randomized benchmarking, generalizes key elements of both character and synthetic randomized benchmarking to benchmark a target group of quantum gates with respect to an enlarged group. We illustrate in numerical examples that our method can efficiently and reliably estimate the fidelity of two-qubit gates relevant to experimental trapped-ion systems. These techniques may find applications beyond randomized benchmarking to quantum tomography and learning, as well as the characterization of error-correcting codes.
Quantum computers have the potential to bring about a new age of technology, but in order for them to become a reality, the elephant in the room must be addressed, quantum errors. The complexity of quantum errors grows exponentially as the system size is increased; scalable characterization protocols which work under physically realistic noise are therefore needed to assess and optimize control. \n \nRandomized Benchmarking (RB) is a family of characterization protocols with the requisite qualities. RB protocols are independent of state preparation and measurement (SPAM) errors, and because they extract partial information about the error profiles in the form of figures of merit, they are scalable in the number of qubits. In this thesis, we study these figures of merit under various error models, gate-sets, and sample distributions, to further our understanding of their physical meaning, and to fine-tune the best practice for diagnosing errors in basic gate-sets. \n \nThe first study presented in this thesis looks at the physical meaning of the unitarity under physically realistic gate-dependent noise. Numerically, we demonstrate that under these realistic noise models, the unitarity obtained via Extended RB (XRB) overlaps strongly with the average of the unitarity of the errors over the set of individual operations. \n \nThe second study numerically and analytically proves that the Standard RB (SRB) decay parameter p coincides with the decay parameter of the novel figure of merit gate-set circuit fidelity. We also prove that, in the limit of high-fidelity single-qubit experiments, the disconnect between the average gate fidelity and SRB experimental results is caused by a basis mismatch between the gates and the state-preparation and measurement procedures. \n \nIn the third part of this thesis, we compare the results of two variations of the SRB protocol, one that samples uniformly (SRB) and one that samples non-uniformly (NIST RB) from the Clifford group. We prove that NIST RB produces an exponential fidelity curve that gives different infidelity results than SRB. \n \nThe fourth and final study gives a standard for assessing basic gate-sets. Experimental results are given from the assessment run on super-conducting and ion-trap devices. We also experimentally show how the systematic error bounds can be tightened by accounting for the error's degree of coherence, as well as using weaker randomizing sets.
Randomized benchmarking is a useful scheme for evaluation the average fidelity of a noisy quantum circuit. However, it is insensitive to the unitary error. Here, we propose a method of randomized benchmarking in which a unitary t-design is applied and by which the unitary error estimation can be converted to analysis of pseudo-randomness on a set of unitary operators. We give a bound on the number of randomized benchmarking sequences, when performing a unitary t-design on n-qubit d-dimensional system. By applying local random unitary operators, a decomposition of a unitary t-design, the bound is more practical than the previous bound for multi-qubit circuit. We also give a rigorous bound of a diamond norm between arbitrary and uniform distributions of a set of unitary operators to form an ε-approximate unitary t-design. It can be used to quantitatively analyze the corresponding average fidelity and errors in a large-scale quantum circuit.
Randomized benchmarking (RB) protocols have become an essential tool for providing a meaningful partial characterization of experimental quantum operations. While the RB decay rate is known to enable estimates of the average fidelity of those operations under gate-independent Markovian noise, under gate-dependent noise this rate is more difficult to interpret rigorously. In this paper, we prove that single-qubit RB experiments provide direct estimates of the gateset circuit fidelity, a novel figure of merit which characterizes the expected average fidelity over arbitrary circuits of operations from the gateset. We also prove that, in the limit of high-fidelity single-qubit experiments, the difficulty introduced by gate-dependence reduces to a basis mismatch between the gates and the state-preparation and measurement procedures, that is, to a unitary degree of freedom in labeling the Pauli matrices. Based on numerical evidence and physically motivated arguments, we conjecture that these result hold for higher dimensions.