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Register a new userRecovering quantum gates from few average gate fidelities
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Characterising quantum processes is a key task in and constitutes a challenge for the development of quantum technologies, especially at the noisy intermediate scale of todays devices. One method for characterising processes is randomised benchmarking, which is robust against state preparation and measurement (SPAM) errors, and can be used to benchmark Clifford gates. A complementing approach asks for full tomographic knowledge. Compressed sensing techniques achieve full tomography of quantum channels essentially at optimal resource efficiency. So far, guarantees for compressed sensing protocols rely on unstructured random measurements and can not be applied to the data acquired from randomised benchmarking experiments. It has been an open question whether or not the favourable features of both worlds can be combined. In this work, we give a positive answer to this question. For the important case of characterising multi-qubit unitary gates, we provide a rigorously guaranteed and practical reconstruction method that works with an essentially optimal number of average gate fidelities measured respect to random Clifford unitaries. Moreover, for general unital quantum channels we provide an explicit expansion into a unitary 2-design, allowing for a practical and guaranteed reconstruction also in that case. As a side result, we obtain a new statistical interpretation of the unitarity -- a figure of merit that characterises the coherence of a process. In our proofs we exploit recent representation theoretic insights on the Clifford group, develop a version of Collins calculus with Weingarten functions for integration over the Clifford group, and combine this with proof techniques from compressed sensing.
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Various quantum applications can be reduced to estimating expectation values, which are inevitably deviated by operational and environmental errors. Although errors can be tackled by quantum error correction, the overheads are far from being affordable for near-term technologies. To alleviate the detrimental effects of errors, quantum error mitigation techniques have been proposed, which require no additional qubit resources. Here, we benchmark the performance of a quantum error mitigation technique based on probabilistic error cancellation in a trapped-ion system. Our results clearly show that effective gate fidelities exceed physical fidelities, i.e. we surpass the break-even point of eliminating gate errors, by programming quantum circuits. The error rates are effectively reduced from $(1.10pm 0.12)times10^{-3}$ to $(1.44pm 5.28)times10^{-5}$ and from $(0.99pm 0.06)times10^{-2}$ to $(0.96pm 0.10)times10^{-3}$ for single- and two-qubit gates, respectively. Our demonstration opens up the possibility of implementing high-fidelity computations on a near-term noisy quantum device.
We report the first complete characterization of single-qubit and two-qubit gate fidelities in silicon-based spin qubits, including cross-talk and error correlations between the two qubits. To do so, we use a combination of standard randomized benchmarking and a recently introduced method called character randomized benchmarking, which allows for more reliable estimates of the two-qubit fidelity in this system. Interestingly, with character randomized benchmarking, the two-qubit CPhase gate fidelity can be obtained by studying the additional decay induced by interleaving the CPhase gate in a reference sequence of single-qubit gates only. This work sets the stage for further improvements in all the relevant gate fidelities in silicon spin qubits beyond the error threshold for fault-tolerant quantum computation.
Predicting properties of complex, large-scale quantum systems is essential for developing quantum technologies. We present an efficient method for constructing an approximate classical description of a quantum state using very few measurements of the state. This description, called a classical shadow, can be used to predict many different properties: order $log M$ measurements suffice to accurately predict $M$ different functions of the state with high success probability. The number of measurements is independent of the system size, and saturates information-theoretic lower bounds. Moreover, target properties to predict can be selected after the measurements are completed. We support our theoretical findings with extensive numerical experiments. We apply classical shadows to predict quantum fidelities, entanglement entropies, two-point correlation functions, expectation values of local observables, and the energy variance of many-body local Hamiltonians. The numerical results highlight the advantages of classical shadows relative to previously known methods.
We utilize a concatenation scheme to construct new families of quantum error correction codes that include the Bacon-Shor codes. We show that our scheme can lead to asymptotically good quantum codes while Bacon-Shor codes cannot. Further, the concatenation scheme allows us to derive quantum LDPC codes of distance $Omega(N^{2/3}/loglog N)$ which can improve Hastingss recent result [arXiv:2102.10030] by a polylogarithmic factor. Moreover, assisted by the Evra-Kaufman-Zemor distance balancing construction, our concatenation scheme can yield quantum LDPC codes with non-vanishing code rates and better minimum distance upper bound than the hypergraph product quantum LDPC codes. Finally, we derive a family of fast encodable and decodable quantum concatenated codes with parameters ${Q}=[[N,Omega(sqrt{N}),Omega( sqrt{N})]]$ and they also belong to the Bacon-Shor codes. We show that ${Q}$ can be encoded very efficiently by circuits of size $O(N)$ and depth $O(sqrt{N})$, and can correct any adversarial error of weight up to half the minimum distance bound in $O(sqrt{N})$ time. To the best of our knowledge, they are the most powerful quantum codes for correcting so many adversarial errors in sublinear time by far.
A pure multipartite quantum state is called absolutely maximally entangled (AME), if all reductions obtained by tracing out at least half of its parties are maximally mixed. Maximal entanglement is then present across every bipartition. The existence of such states is in many cases unclear. With the help of the weight enumerator machinery known from quantum error correction and the generalized shadow inequalities, we obtain new bounds on the existence of AME states in dimensions larger than two. To complete the treatment on the weight enumerator machinery, the quantum MacWilliams identity is derived in the Bloch representation. Finally, we consider AME states whose subsystems have different local dimensions, and present an example for a $2 times3 times 3 times 3$ system that shows maximal entanglement across every bipartition.
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