Variational Quantum Algorithms (VQAs) rely upon the iterative optimization of a parameterized unitary circuit with respect to an objective function. Since quantum machines are noisy and expensive resources, it is imperative to choose a VQA's ansatz appropriately and its initial parameters to be close to optimal.
This work tackles the problem of finding initial ansatz parameters by proposing CAFQA, a Clifford ansatz for quantum accuracy. The CAFQA ansatz is a hardware-efficient circuit built with only Clifford gates. In this ansatz, the initial parameters for the tunable gates are chosen by searching efficiently through the Clifford parameter space via classical simulation, thereby producing a suitable stabilizer state. The stabilizer states produced are shown to always equal or outperform traditional classical initialization (e.g., Hartree-Fock), and often produce high accuracy estimations prior to quantum exploration. Furthermore, the technique is classically suited since a) Clifford circuits can be exactly simulated classically in polynomial time and b) the discrete Clifford space, while scaling exponentially in the number of qubits, is searched efficiently via Bayesian Optimization.
For the Variational Quantum Eigensolver (VQE) task of molecular ground state energy estimation up to 20 qubits, CAFQA's Clifford Ansatz achieves a mean accuracy of near 99%, recovering as much as 99.99% of the correlation energy over Hartree-Fock. Notably, the scalability of the approach allows for preliminary ground state energy estimation of the challenging Chromium dimer with an accuracy greater than Hartree-Fock. With CAFQA's initialization, VQA convergence is accelerated by a factor of 2.5x.
In all, this work shows that stabilizer states are an accurate ansatz initialization for VQAs. Furthermore, it highlights the potential for quantum-inspired classical techniques to support VQAs.
more »
« less
Quantifying the magic of quantum channels
To achieve universal quantum computation via general fault-tolerant schemes, stabilizer operations must be supplemented with other non-stabilizer quantum resources. Motivated by this necessity, we develop a resource theory for magic quantum channels to characterize and quantify the quantum ‘magic’ or non-stabilizerness of noisy quantum circuits. For qudit quantum computing with odd dimension
- Award ID(s):
- 1714215
- NSF-PAR ID:
- 10308394
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- New Journal of Physics
- Volume:
- 21
- Issue:
- 10
- ISSN:
- 1367-2630
- Page Range / eLocation ID:
- Article No. 103002
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Quantum computers have the potential to provide exponential speedups over their classical counterparts. Quantum principles are being applied to fields such as communications, information processing, and artificial intelligence to achieve quantum advantage. However, quantum bits are extremely noisy and prone to decoherence. Thus, keeping the qubits error free is extremely important toward reliable quantum computing. Quantum error correcting codes have been studied for several decades and methods have been proposed to import classical error correcting codes to the quantum domain. Along with the exploration into novel and more efficient quantum error correction codes, it is also essential to design circuits for practical realization of these codes. This paper serves as a tutorial on designing and simulating quantum encoder and decoder circuits for stabilizer codes. We first describe Shor’s 9-qubit code which was the first quantum error correcting code. We discuss the stabilizer formalism along with the design of encoding and decoding circuits for stabilizer codes such as the five-qubit code and Steane code. We also design nearest neighbor compliant circuits for the above codes. The circuits were simulated and verified using IBM Qiskit.more » « less
-
Improving the simulation of quantum circuits on classical computers is important for understanding quantum advantage and increasing development speed. In this paper, we explore a way to express stabilizer states and further improve the speed of simulating stabilizer circuits with a current existing approach. First, we discover a unique and elegant canonical form for stabilizer states based on graph states to better represent stabilizer states and show how to efficiently simplify stabilizer states to canonical form. Second, we develop an improved algorithm for graph state stabilizer simulation and establish limitations on reducing the quadratic runtime of applying controlled Pauli Z gates. We do so by creating a simpler formula for combining two Pauli-related stabilizer states into one. Third, to better understand the linear dependence of stabilizer states, we characterize all linearly dependent triplets, revealing symmetries in the inner products. Using our controlled Pauli Z algorithm, we improve runtime for inner product computation from O(n^3) to O(nd^2), where d is the maximum degree of the graph encountered during the calculation.more » « less
-
Large multipartite quantum systems tend to rapidly reach extraordinary levels of complexity as their number of constituents and entanglement links grow. Here we use complex network theory to study a class of continuous variables quantum states that present both multipartite entanglement and non-Gaussian statistics. In particular, the states are built from an initial imprinted cluster state created via Gaussian entangling operations according to a complex network structure. To go beyond states that can be easily simulated via classical computers we engender non-Gaussian statistics via multiple photon subtraction operations. We then use typical networks measures, the degree and clustering, to characterize the emergent complex network of photon-number correlations after photon subtractions. We show that, in contrast to regular clusters, in the case of imprinted complex network structures the emergent correlations are strongly affected by photon subtraction. On the one hand, we unveil that photon subtraction universally increases the average photon-number correlations, regardless of the imprinted network structure. On the other hand, we show that the shape of the distributions in the emergent networks after subtraction is greatly influenced by the structure of the imprinted network, as witnessed by their higher-moments. Thus for the field of network theory, we introduce a new class of networks to study. At the same time for the field of continuous variable quantum states, this work presents a new set of practical tools to benchmark systems of increasing complexity.more » « less
-
The challenge of quantum computing is to combine error resilience with universal computation. Diagonal gates such as the transversal T gate play an important role in implementing a universal set of quantum operations. This paper introduces a framework that describes the process of preparing a code state, applying a diagonal physical gate, measuring a code syndrome, and applying a Pauli correction that may depend on the measured syndrome (the average logical channel induced by an arbitrary diagonal gate). It focuses on CSS codes, and describes the interaction of code states and physical gates in terms of generator coefficients determined by the induced logical operator. The interaction of code states and diagonal gates depends very strongly on the signs of Z -stabilizers in the CSS code, and the proposed generator coefficient framework explicitly includes this degree of freedom. The paper derives necessary and sufficient conditions for an arbitrary diagonal gate to preserve the code space of a stabilizer code, and provides an explicit expression of the induced logical operator. When the diagonal gate is a quadratic form diagonal gate (introduced by Rengaswamy et al.), the conditions can be expressed in terms of divisibility of weights in the two classical codes that determine the CSS code. These codes find application in magic state distillation and elsewhere. When all the signs are positive, the paper characterizes all possible CSS codes, invariant under transversal Z -rotation through π / 2 l , that are constructed from classical Reed-Muller codes by deriving the necessary and sufficient constraints on l . The generator coefficient framework extends to arbitrary stabilizer codes but there is nothing to be gained by considering the more general class of non-degenerate stabilizer codes.more » « less
