scholarly journals Quantum computed moments correction to variational estimates

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 373
Author(s):  
Harish J. Vallury ◽  
Michael A. Jones ◽  
Charles D. Hill ◽  
Lloyd C. L. Hollenberg
Keyword(s):  
Quantum Circuit ◽  
Variational Calculation ◽  
Order Effects ◽  
Quantum Magnetism ◽  
Superconducting Qubit ◽  
Problem Size ◽  
Variational Calculations ◽  
State Variation ◽  
Random Coupling ◽  
Trial State

The variational principle of quantum mechanics is the backbone of hybrid quantum computing for a range of applications. However, as the problem size grows, quantum logic errors and the effect of barren plateaus overwhelm the quality of the results. There is now a clear focus on strategies that require fewer quantum circuit steps and are robust to device errors. Here we present an approach in which problem complexity is transferred to dynamic quantities computed on the quantum processor – Hamiltonian moments, ⟨Hn⟩. From these quantum computed moments, an estimate of the ground-state energy can be obtained using the ``infimum'' theorem from Lanczos cumulant expansions which manifestly corrects the associated variational calculation. With higher order effects in Hilbert space generated via the moments, the burden on the trial-state quantum circuit depth is eased. The method is introduced and demonstrated on 2D quantum magnetism models on lattices up to 5×5 (25 qubits) implemented on IBM Quantum superconducting qubit devices. Moments were quantum computed to fourth order with respect to a parameterised antiferromagnetic trial-state. A comprehensive comparison with benchmark variational calculations was performed, including over an ensemble of random coupling instances. The results showed that the infimum estimate consistently outperformed the benchmark variational approach for the same trial-state. These initial investigations suggest that the quantum computed moments approach has a high degree of stability against trial-state variation, quantum gate errors and shot noise, all of which bodes well for further investigation and applications of the approach.

scholarly journals Variational Solution of the Gross–Neveu Model: Finite N and Renormalization

1997 ◽  
Vol 12 (19) ◽  
pp. 3307-3334 ◽  
Author(s):  
C. Arvanitis ◽  
F. Geniet ◽  
M. Iacomi ◽  
J.-L. Kneur ◽  
A. Neveu
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
General Framework ◽  
Free Field ◽  
Variational Calculation ◽  
Final Point ◽  
Variational Calculations ◽  
Perturbative Renormalization ◽  
Good Agreement ◽  
Gross Neveu Model

We show how to perform systematically improvable variational calculations in the O(2N) Gross–Neveu model for generic N, in such a way that all infinities usually plaguing such calculations are accounted for in a way compatible with the perturbative renormalization group. The final point is a general framework for the calculation of nonperturbative quantities like condensates, masses, etc., in an asymptotically free field theory. For the Gross–Neveu model, the numerical results obtained from a "two-loop" variational calculation are in a very good agreement with exact quantities down to low values of N.

Experimental demonstration of optimized quantum process tomography on the IBM quantum experience

2020 ◽  
pp. 2040004
Author(s):  
Akshay Gaikwad ◽  
Krishna Shende ◽  
Kavita Dorai
Keyword(s):  
Quantum Circuit ◽  
Quantum Gates ◽  
Experimental Demonstration ◽  
Superconducting Qubit ◽  
Quantum Process ◽  
Single Qubit ◽  
Quantum Process Tomography ◽  
Process Tomography ◽  
Quantum Processor ◽  
Least Squares Optimization

We experimentally performed complete and optimized quantum process tomography of quantum gates implemented on superconducting qubit-based IBM QX2 quantum processor via two constrained convex optimization (CCO) techniques: least squares optimization and compressed sensing optimization. We studied the performance of these methods by comparing the experimental complexity involved and the experimental fidelities obtained. We experimentally characterized several two-qubit quantum gates: identity gate, a controlled-NOT gate, and a SWAP gate. The general quantum circuit is efficient in the sense that the data needed to perform CCO-based process tomography can be directly acquired by measuring only a single qubit. The quantum circuit can be extended to higher dimensions and is also valid for other experimental platforms.

scholarly journals Hybrid Quantum Circuit with a Superconducting Qubit Coupled to a Spin Ensemble

2011 ◽  
Vol 107 (22) ◽  
Author(s):  
Y. Kubo ◽  
C. Grezes ◽  
A. Dewes ◽  
T. Umeda ◽  
J. Isoya ◽  
...  
Keyword(s):  
Quantum Circuit ◽  
Superconducting Qubit

scholarly journals Erratum: Micromachined Integrated Quantum Circuit Containing a Superconducting Qubit [Phys. Rev. Applied 7 , 044018 (2017)]

2017 ◽  
Vol 8 (3) ◽  
Author(s):  
T. Brecht ◽  
Y. Chu ◽  
C. Axline ◽  
W. Pfaff ◽  
J. Z. Blumoff ◽  
...  
Keyword(s):  
Quantum Circuit ◽  
Superconducting Qubit

scholarly journals Improved Superconducting Qubit State Readout by Path Interference

2021 ◽  
Vol 38 (11) ◽  
pp. 110303
Author(s):  
Zhiling Wang ◽  
Zenghui Bao ◽  
Yukai Wu ◽  
Yan Li ◽  
Cheng Ma ◽  
...  
Keyword(s):  
Quantum Information Processing ◽  
Quantum Circuit ◽  
Qubit State ◽  
Microwave Cavity ◽  
Single Shot ◽  
Superconducting Qubit ◽  
Constructive Interference ◽  
State Discrimination ◽  
Convenient Approach ◽  
Photon States

High fidelity single shot qubit state readout is essential for many quantum information processing protocols. In superconducting quantum circuit, the qubit state is usually determined by detecting the dispersive frequency shift of a microwave cavity from either transmission or reflection. We demonstrate the use of constructive interference between the transmitted and reflected signal to optimize the qubit state readout, with which we find a better resolved state discrimination and an improved qubit readout fidelity. As a simple and convenient approach, our scheme can be combined with other qubit readout methods based on the discrimination of cavity photon states to further improve the qubit state readout.

scholarly journals An Ising Hamiltonian Solver using Stochastic Phase-Transition Nano-Oscillators

2020 ◽  
Author(s):  
Sourav Dutta ◽  
Abhishek Khanna ◽  
Hanjong Paik ◽  
Darrell Schlom ◽  
Arijit Raychowdhury ◽  
...  
Keyword(s):  
Phase Transition ◽  
Ground State ◽  
Cyber Security ◽  
Optimal Solution ◽  
Ground State Solution ◽  
Hopfield Network ◽  
Superconducting Qubit ◽  
Problem Size ◽  
Order Of Magnitude ◽  
Magnitude Improvement

Abstract Computationally hard problems, including combinatorial optimization, can be mapped into the problem of finding the ground-state of an Ising Hamiltonian. Building physical systems with collective computational ability and distributed parallel processing capability can accelerate the ground-state search. Here, we present a continuous-time dynamical system (CTDS) approach where the ground-state solution appears as stable points or attractor states of the CTDS. We harness the emergent dynamics of a network of phase-transition nano-oscillators (PTNO) to build an Ising Hamiltonian solver. The hardware fabric comprises of electrically coupled injection-locked stochastic PTNOs with bi-stable phases emulating artificial Ising spins. We demonstrate the ability of the stochastic PTNO-CTDS to progressively find more optimal solution by increasing the strength of the injection-locking signal – akin to performing classical annealing. We demonstrate in silico that the PTNO-CTDS prototype solves a benchmark non-deterministic polynomial time (NP)-hard Max-Cut problem with high probability of success. Using experimentally calibrated numerical simulations, we investigate the performance of the hardware with increasing problem size. We show the best-in-class energy-efficiency of 3.26x107 solutions/sec/Watt which translates to over five orders of magnitude improvement when compared with digital CMOS, superconducting qubit and photonic Ising solver approaches. We also demonstrate an order of magnitude improvement over a discrete-time memristor-based Hopfield network approach. Such an energy efficient CTDS hardware exhibiting high solution-throughput/Watt can find application in industrial planning and manufacturing, defense and cyber-security, bioinformatics and drug discovery.

scholarly journals Robustly decorrelating errors with mixed quantum gates

2021 ◽  
Author(s):  
Anthony Polloreno ◽  
Kevin Young
Keyword(s):  
Optimal Control ◽  
Quantum Information ◽  
Marked Reduction ◽  
Quantum Circuit ◽  
Physical Review ◽  
Quantum Gates ◽  
Superconducting Qubit ◽  
Convex Programs ◽  
Quantum Operations ◽  
Quantum Optimal Control

Abstract Coherent errors in quantum operations are ubiquitous. Whether arising from spurious environmental couplings or errors in control fields, such errors can accumulate rapidly and degrade the performance of a quantum circuit significantly more than an average gate fidelity may indicate. As shown by Hastings [1] and Campbell [2], by replacing the deterministic implementation of a quantum gate with a randomized ensemble of implementations, one can dramatically suppress coherent errors. Our work begins by reformulating the results of Hastings and Campbell as a quantum optimal control problem. We then discuss a family of convex programs able to solve this problem, as well as a set of secondary objectives designed to improve the performance, implementability, and robustness of the resulting mixed quantum gates. Finally, we implement these mixed quantum gates on a superconducting qubit and discuss randomized benchmarking results consistent with a marked reduction in the coherent error. [1] M. B. Hastings, Quantum Information & Computation 17, 488 (2017). [2] E. Campbell, Physical Review A 95, 042306 (2017).

scholarly journals Micromachined Integrated Quantum Circuit Containing a Superconducting Qubit

2017 ◽  
Vol 7 (4) ◽  
Author(s):  
T. Brecht ◽  
Y. Chu ◽  
C. Axline ◽  
W. Pfaff ◽  
J. Z. Blumoff ◽  
...  
Keyword(s):  
Quantum Circuit ◽  
Superconducting Qubit
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