US-12626173-B2 - Device and method for continuous time quantum computing

Abstract

The present disclosure relates to quantum computing methods and devices, wherein a computation corresponding to a certain desired unitary transformation of the Hilbert space of a quantum system, such as a set of qubits, is implemented by selective application of control pulses in order realize a continuous time quantum computation rather than by decomposing the unitary transformation into a sequence of gates taken from a fixed set of gates. In this way an effective Hamiltonian having an input matrix A encoded as an off-diagonal block connecting a first and a second subspace of the quantum system is then applied alternatingly with some standard Hamiltonian in order to obtain a time evolution corresponding to a given function f applied to the input matrix A. The required control pulses are optimized by means of classical compression techniques such as a deep learning neural network, in order to maximize, during the information loading phase of the computation, the amount of classical information loaded into the system, and, during the computational phase, the number of elementary continuous time quantum transformations, respectively.

Inventors

• Michele Reilly
• Seth Lloyd

Assignees

• Second Foundation, Inc.

Dates

Publication Date

20260512

Application Date

20220310

Claims (4)

1. 1 . A quantum computing device, comprising: a quantum system providing a computational Hilbert space having a first subspace of dimension D 1 and a second subspace of dimension D 2 , a number K≥1 of control field generators, each control field generator capable of generating a semi-classical control field, wherein a Hamiltonian applied to the quantum system depends on the control fields, and a classical control system controlling the control field generators, wherein the classical control system is able to: by means of a first sequence of control field settings, apply to the quantum system a first effective Hamiltonian (H eff ) having, in computational bases of the first and second subspace, a matrix representation with an off-diagonal block corresponding to an input matrix A of shape D 1 ×D 2 having a singular value decomposition A = ∑ j = 1 J ⁢ σ j ❘ "\[LeftBracketingBar]" i j 〉〈 r j ❘ "\[RightBracketingBar]" with a number J of non-zero singular values σ j , left singular vectors |l j from the first subspace and right singular vectors r j | from the second subspace, and by means of a second sequence of control field settings, apply to the quantum system a second effective Hamiltonian having a matrix representation of the form Z = I 1 - I 2 ⁢ where ⁢ I 1 = ∑ j = 1 J ❘ "\[LeftBracketingBar]" l j 〉〈 l f ❘ "\[RightBracketingBar]" 1 and I 2 = ∑ j = 1 J ❘ "\[LeftBracketingBar]" r j 〉〈 r j ❘ "\[RightBracketingBar]" 1 , such that the second effective Hamiltonian (Z) induces a phase rotation in two dimensional subspaces spanned by two computational Hilbert space vectors, where one of the vectors is taken from the first subspace and the other is taken from the second subspace, wherein, in order to obtain unitary evolution of the quantum system having, in a matrix representation in the computational bases of the first and second subspace, an off-diagonal block corresponding to a given function f (A) of the input matrix A, the classical control system is configured to perform the steps: (a) apply the second effective Hamiltonian for a first phase rotation time corresponding to a phase rotation by a first angle (Φ 1 ), then (b) apply the first effective Hamiltonian for a first time (t 1 ), and then (c) apply again the second effective Hamiltonian for a phase rotation time corresponding to a phase rotation by the negative of the first angle or apply the negative of the second effective Hamiltonian for the first phase rotation time, thereby effecting a unitary transformation e −iG Φ1 t 1 :=e iΦ 1 Z e −i Heff t 1 e −iΦ1Z , wherein the classical control system is further configured to repeat the steps a-c for a second, third and so on up to a L-th angle Φ L and a second, third and so on up to a L-th time t L thereby effecting a unitary transformation U HOSVT =e −iG ΦL t L e −iG ΦL-1 t L-1 . . . e −iG Φ1 t 1 , a classical preprocessing system that carries out an optimization of the first, second third and so on rotation angles Φ L and times t L , wherein the classical preprocessing system comprises a neural network, in particular a generative neural network, wherein the optimization involves a gradient descent on weights of the neural network, wherein the optimization involves feeding the function f(A) or its singular value decomposition to an input layer of the neural network.
2. 2 . The device of claim 1 , wherein the preprocessing system is comprised in the classical control system.
3. 3 . A method for performing quantum computation in a quantum computing device, the method comprising comprising: providing, by a quantum system, a computational Hilbert space having a first subspace of dimension D 1 and a second subspace of dimension D 2 , generating, by at least one control field generator, a number K>1 of semi-classical control fields, wherein a Hamiltonian applied to the quantum system depends on the control fields, by means of a first sequence of control field settings, applying to the quantum system a first effective Hamiltonian (H eff ) having a matrix representation with an off-diagonal block corresponding to an input matrix A of shape D 1 ×D 2 , and by means of a second sequence of control field settings, applying to the quantum system a second effective Hamiltonian (Z) having a matrix representation of the form Z=I 1 −I 2 where I 1 = ∑ j = 1 J ❘ "\[LeftBracketingBar]" l j 〉〈 l j ❘ "\[RightBracketingBar]" 1 , and I 2 = I 2 = ∑ j = 1 J ❘ "\[LeftBracketingBar]" r j 〉〈 r j ❘ "\[RightBracketingBar]" 1 , such that the second effective Hamiltonian induces a phase rotation in two dimensional subspaces spanned by two computational Hilbert space vectors, where one of the vectors is taken from the first subspace and the other is taken from the second subspace, the method further comprising the steps: (a) applying the second effective Hamiltonian Z for a first phase rotation time corresponding to a phase rotation by a first angle (Φ 1 ) then (b) applying the first effective Hamiltonian H eff for a first time t 1 , and then (c) applying again the second Hamiltonian Z for a phase rotation time corresponding to a phase rotation by the negative of the first angle or applying the negative of the second Hamiltonian for the first phase rotation time, thereby effecting a unitary transformation e −iG Φ1 t 1 :=e iΦ 1 Z e −i Heff t 1 e −iΦ1Z , wherein the steps a-c are repeated for a second, third and so on up to a L-th angle Φ L and a second, third and so on up to a L-th time t L thereby effecting a unitary transformation U HOSVT =e −iG ΦL t L e −iG ΦL-1 t L-1 . . . e −iG Φ1 t 1 , carrying out an optimization of the first, second third and so on rotation angles Φ L and times t L in a classical preprocessing step, wherein the classical preprocessing step comprises a neural network, in particular a generative neural network, wherein the optimization involves a gradient descent on weights of the neural network, wherein the optimization involves feeding the function f(A) or its singular value decomposition to an input layer of the neural network.
4. 4 . The method of claim 3 , wherein the preprocessing step is carried out by a classical control system of the quantum computing device.

Description

CROSS-REFERENCE TO RELATED APPLICATION This application is the United States national phase of International Application No. PCT/EP2022/056176 filed Mar. 10, 2022, the disclosure of which is hereby incorporated by reference in its entirety. BACKGROUND OF THE INVENTION Field of the Invention The present disclosure relates to methods and devices for performing quantum computations. Description of Related Art A quantum computer is a device that processes information stored on quantum mechanical degrees of freedom, such as atoms, electrons, photons and superconducting qubits. Quantum information partakes in the strange and counterintuitive features of quantum mechanics: quantum bits can exist in superpositions of 0 and 1, and two or more quantum degrees of freedom can be entangled, exhibiting what Einstein called ‘spooky action at a distance’. Quantum computers employ the strange and counterintuitive features of quantum mechanics to process information in ways that classical computers can't, thereby achieving substantial potential speedups over classical computers for a variety of problems. Like nearly all modern classical computers, quantum computers are usually digital computers storing information in arrays of two state systems or qubits. With each qubit spanning a two dimensional Hilbert space, the total computational Hilbert space of an N-qubit register is 2N, which is the dimension of the product space of the Hilbert spaces of the individual qubits. While it is possible to also use three or more state systems, i.e. qutrits, ququads etc., in place or in addition to qubits, these offer at most practical but no fundamental benefits. It is also possible to perform quantum information processing on systems such as harmonic oscillators or modes of the electromagnetic field that possess continuous degrees of freedom. Another analogy carried over from classical computers due to its conceptual simplicity is the use of gates, i.e. basic quantum operations on one, two or more qubits in the description of quantum processing operations to be performed in a quantum computer. Any pure quantum computation run on a quantum computer can be described by a global unitary operation on its computational Hilbert space. A quantum algorithm that achieves some quantum computational task, such as Grover's search algorithm, Shor's factorization algorithm or quantum Fourier transform, usually also includes preparation and measurement steps, but in between these projective operations a pure unitary evolution takes place. Just as any classical computation can be broken down into a sequence of basic logic operations or gates on the classical bits of a classical digital computer, it was established early during quantum computation research that any unitary operation can be arbitrarily closely realized by sequences of one- and two-qubit gates taken from a small set of gates acting on the qubits of the quantum computer. This quantum circuit model has been in use since the inception of quantum computation and nearly all quantum computer concepts are based on it. Being carried over from classical digital computing, it has the benefit of easy adoption by those already working in the field, as well as being straightforward to learn for newcomers as it allows a LEGO®-like approach to thinking about computation. Most importantly, however, by its restriction to a finite and rather small set of basic operations, it allows straightforward proofs of the computational completeness of a particular quantum computing implementation (as one just needs to implement each gate of the basic set) as well as more easily proving theorems about completeness and optimality of algorithms. The circuit model of quantum computation has, however, the downside of being, in general, far from resource optimal. Since all quantum information in a quantum computer is subject to some degree of decoherence and the quantum gates of a computer also have a certain failure probability, error correction techniques are far more important in quantum computing than in classical computing: whereas in the latter there is usually a large energy barrier separating two distinct states of a classical bit, even a small influence can change the state of a qubit, in case of the phase information even without costing any energy (if the computational basis states are also energy eigenstates of the native system Hamiltonian, as is usually the case). In circuit model quantum computing intricate error correction schemes have therefore been devised to cope with this problem. They all achieve this by using logical qubits encoded in multiple physical qubits, thereby adding redundancy such that a single or a small number of errors in the physical qubits does not compromise the stored logical quantum information. Error correction adds a significant overhead. For current devices and depending on the architecture, it is required for computations using on the order of a thousand gates or more. However, ev