Multiqubit randomized benchmarking using few samples

Helsen, Jonas; Wallman, Joel J.; Flammia, Steven T.; Wehner, Stephanie

doi:10.1103/physreva.100.032304

Cited by 49 publications

(76 citation statements)

References 66 publications

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“…For each RB sequence, we randomly select the recovery operation to either return the qubit to |0 (as in conventional RB) or |1 , keeping track of which recovery was used while still making the experiment "blind" to the correct final state. Similar modifications to the recovery operation have been studied in other leakage-detecting variants of RB [6,7,26,27]. The measurement probabilities as a function of N are binned in two groups y 0 and y 1 , where the subscript denotes the selection of recovery operation, as shown in Fig.…”

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confidence: 99%

Quantifying error and leakage in an encoded Si/SiGe triple-dot qubit

et al. 2019

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Quantum computation requires qubits that satisfy often-conflicting criteria, including scalable control and long-lasting coherence [1]. One approach to creating a suitable qubit is to operate in an encoded subspace of several physical qubits. Though such encoded qubits may be particularly susceptible to leakage out of their computational subspace, they can be insensitive to certain noise processes [2, 3] and can also allow logical control with a single type of entangling interaction [4] while maintaining favorable features of the underlying physical system. Here we demonstrate a qubit encoded in a subsystem of three coupled electron spins confined in gated, isotopically enhanced silicon quantum dots [4, 5]. Using a modified "blind" randomized benchmarking protocol that determines both computational and leakage errors [6, 7], we show that unitary operations have an average total error of 0.35%, with 0.17% of that coming from leakage driven by interactions with substrate nuclear spins. This demonstration utilizes only the voltage-controlled exchange interaction for qubit manipulation and highlights the operational benefits of encoded subsystems, heralding the realization of high-quality encoded multi-qubit operations [4, 8].Electrons trapped in silicon heterostructures have many attractive features, including very long coherence times in isotopically enriched material [9, 10] and compatibility with standard fabrication techniques. Singlespin qubits have recently demonstrated high-fidelity RFcontrolled single-qubit operations [10, 11] and two-qubit gates using the exchange interaction [12][13][14]. However, using RF signals for single-qubit control requires a large, stable magnetic field and introduces challenges with crosstalk. Fortunately, electron spins are particularly well-suited to forming encoded qubits. Two coupled electron spins can be operated at near-zero magnetic field as a "singlet-triplet" qubit [15,16]. That qubit is insensitive to uniform magnetic field fluctuations but still requires a magnetic field gradient for universal control. Three coupled electrons [17] can form a qubit with a tunable electric dipole moment, which could enhance RF selectivity, or the exchange-only qubit, which can be universally controlled using only the exchange interaction and does not require synchronization of gate operations with a local oscillator. Exchange is highly local and can be accurately controlled with a large on-off ratio using only fast voltage pulses. The combination of these features makes the exchange-only qubit especially attractive b X2

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confidence: 99%

Quantifying error and leakage in an encoded Si/SiGe triple-dot qubit

et al. 2019

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“…(Note that we do not simplify circuits to their optimal form here but simply report the results of our synthesis algorithm.) An alternative procedure is to directly input the final symplectic matrix (51) to the symplectic decomposition algorithm in [35] (also see [41, Section II]), yielding the following circuit (CKT2). [3,4] The difference in depth of the two circuits is very small in this case, but we found that for about half of the elements in P K,4 the explicit form in Corollary 24 had smaller depth, while for those remaining, the direct decomposition was better.…”

Section: Logical Unitary 2-designsmentioning

confidence: 99%

Kerdock Codes Determine Unitary 2-Designs

Can

Rengaswamy

Calderbank

et al. 2019

2019 IEEE International Symposium on Information Theory (ISIT)

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The non-linear binary Kerdock codes are known to be Gray images of certain extended cyclic codes of length N = 2 m over Z4. We show that exponentiating these Z4-valued codewords by ı √ −1 produces stabilizer states, that are quantum states obtained using only Clifford unitaries. These states are also the common eigenvectors of commuting Hermitian matrices forming maximal commutative subgroups (MCS) of the Pauli group. We use this quantum description to simplify the derivation of the classical weight distribution of Kerdock codes. Next, we organize the stabilizer states to form N + 1 mutually unbiased bases and prove that automorphisms of the Kerdock code permute their corresponding MCS, thereby forming a subgroup of the Clifford group. When represented as symplectic matrices, this subgroup is isomorphic to the projective special linear group PSL(2, N ). We show that this automorphism group acts transitively on the Pauli matrices, which implies that the ensemble is Pauli mixing and hence forms a unitary 2-design. The Kerdock design described here was originally discovered by Cleve et al. (2016), but the connection to classical codes is new which simplifies its description and translation to circuits significantly. Sampling from the design is straightforward, the translation to circuits uses only Clifford gates, and the process does not require ancillary qubits. Finally, we also develop algorithms for optimizing the synthesis of unitary 2-designs on encoded qubits, i.e., to construct logical unitary 2-designs. Software implementations are available at https://github.com/nrenga/symplectic-arxiv18a, which we use to provide empirical gate complexities for up to 16 qubits.

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“…In randomized benchmarking one must sample M random sequences for each sequence length k ∈ [0 : K], yielding M × (K + 1) experiments. This M is independent of the number of qubits [24]. In experiments M is often chosen between M ≈ 40 [25,26] at the low end and M ≈ 150 at the higher end [27].…”

Section: Resourcesmentioning

confidence: 99%

Spectral quantum tomography

2019

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We introduce spectral quantum tomography, a simple method to extract the eigenvalues of a noisy few-qubit gate, represented by a trace-preserving superoperator, in a SPAM-resistant fashion, using low resources in terms of gate sequence length. The eigenvalues provide detailed gate information, supplementary to known gate-quality measures such as the gate fidelity, and can be used as a gate diagnostic tool. We apply our method to one-and two-qubit gates on two different superconducting systems available in the cloud, namely the QuTech Quantum Infinity and the IBM Quantum Experience. We discuss how cross-talk, leakage and non-Markovian errors affect the eigenvalue data.

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Multiqubit randomized benchmarking using few samples

Cited by 49 publications

References 66 publications

Quantifying error and leakage in an encoded Si/SiGe triple-dot qubit

Quantifying error and leakage in an encoded Si/SiGe triple-dot qubit

Kerdock Codes Determine Unitary 2-Designs

Spectral quantum tomography

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