Trading t-gates for qubits in arbitrary state and unitary synthesis
Efficient synthesis of arbitrary quantum states and unitaries from a universal fault tolerant gate-set (e.g., Clifford+T) is a goal in quantum computation. As physical quantum computers are fixed in size, all available qubits should be used if it minimizes overall gate counts, especially that of the expensive T-gates. In this application, a quantum algorithm is described for preparing any dimension-N quantum state specified by a list of N classical numbers, that realizes a trade-off between space and T-gates. Example embodiments exploit (λ) ancilla qubits, to reduce the T-gate cost to 𝔒 ( N λ + λlog 2 N ϵ ) . Notably, this it proven to be optimal up to logarithmic factors for any λ=o(√{square root over (N)}) through an unconditional gate counting argument. Though (N) Clifford gates are always required, only (√{square root over (N)}) T-gates are needed in the best case, which is a quadratic improvement over prior art. Similar statements are provien for unitary synthesis by reduction to state preparation.
1. A method, comprising:
inputting a quantum algorithm description in a high-level functional language to a classical computer;
with the classical computer, synthesizing the quantum algorithm description into a synthesized quantum circuit representation, wherein the quantum circuit representation is implementable on a quantum computing device, and wherein the synthesizing comprises assigning one or more ancilla qubits to be used for at least one non-Clifford operation and the ancilla qubits to be used for at least one non-Clifford operation replace at least one Toffoli-gate; and
outputting the quantum circuit representation.
2. The method of claim 1 , wherein the synthesized quantum circuit representation includes a combination of both Toffoli gates and ancilla qubits to perform non-Clifford operations, the combination being determined at least in part by a user-selectable variable.
3. The method of claim 1 , wherein the method reduces non-Clifford gates at a cost of greater overall ancilla qubits.
4. The method of claim 1 , wherein the method is performed to synthesize arbitrary unitaries.
5. The method of claim 1 , further comprising controlling a quantum computing device to implement the quantum circuit representations.
6. A method, comprising:
inputting a quantum algorithm description in a high--level functional language to a classical computer;
with the classical computer, synthesizing the quantum algorithm description into a synthesized quantum circuit representation, wherein the quantum circuit representation is implementable on a quantum computing device, and wherein the synthesizing comprises assigning one or more ancilla qubits to be used for at least one non-Clifford operation and the synthesizing comprises using a select-swap operation that enables sublinear T-gate complexity; and
outputting the quantum circuit representation.
7. The method of claim 6 , wherein the select-swap operation results from a combination of a select operation and a swap network.
8. A method, comprising:
inputting a quantum algorithm description in a high-level functional language to a classical computer;
with the classical computer, synthesizing the quantum algorithm description into a synthesized quantum circuit representation, wherein the quantum circuit representation is implementable on a quantum computing device, and wherein the synthesizing comprises assigning one or more ancilla qubits to be used for at least one non-Clifford operation and the synthesizing implements a data-lookup oracle using a select-swap operation; and
outputting the quantum circuit representation.
9. One or more computer-readable memory or storage devices storing computer-executable instructions, which when executed by a classical computer cause the classical computer to perform a method of controlling a quantum computing device, the method comprising:
inputting a high-level functional language description of the quantum algorithm;
synthesizing the functional language description of the quantum algorithm into low-level machine instructions for implementation on a quantum computing device, the low-level machine instructions being implementable on the quantum computing device, and wherein the synthesizing comprises assigning one or more ancilla qubits to be used for at least one non-Clifford operation and wherein the ancilla qubits to be used for at least one non-Clifford operation replace at least one Toffoli-gate; and
controlling the quantum computing device to implement the low-level machine instructions.
10. The one or more computer-readable memory or storage devices of claim 9 , wherein the synthesizing implements a data-lookup oracle using a select-swap operation.
11. The one or more computer-readable memory or storage devices of claim 9 , wherein the method is performed to synthesize arbitrary unitaries.
12. The one or more computer-readable memory or storage devices of claim 9 , wherein the method further comprises controlling a quantum computing device to implement the low-level machine instructions.
13. A system, comprising:
a classical computer; and
one or more computer-readable memory or storage devices storing computer-executable instructions, which when executed by the classical computer cause the classical computer to perform a method of controlling a quantum computing device, the method comprising:
inputting a high-level functional language description of the quantum algorithm;
synthesizing the high-level functional language description of the quantum algorithm into low-level machine instructions on a quantum computing device, the low-level machine instructions being implementable on the quantum computing device, and wherein the synthesizing comprises assigning one or more ancilla qubits to be used for at least one non-Clifford operation and assigning a combination of both Toffoli gates and ancilla qubits to perform non-Clifford operations, the combination being determined at least in part by a user-selectable variable.
14. The system of claim 13 , wherein the method further comprises controlling the quantum computing device to implement the low-level machine instructions.
15. A system, comprising:
a classical computer; and
one or more computer-readable memory or storage devices storing computer-executable instructions, which when executed by the classical computer cause the classical computer to perform a method of controlling a quantum computing device, the method comprising:
inputting a high-level functional language description of the quantum algorithm
synthesizing the high-level functional language description of the quantum algorithm into low-level machine instructions on a quantum computing device, the low-level machine instructions being implementable on the quantum computing device, and wherein the synthesizing comprises assigning one or more ancilla qubits to be used for at least one non-Clifford operation and wherein the synthesizing comprises using a select-swap operation and the select-swap operation enables sublinear T-gate complexity; and
controlling the quantum computing device to implement the low-level machine instructions.
16. The system of claim 15 , wherein the select-swap operation results from a combination of a select operation and a swap network.
17. A quantum circuit comprising a combination of Clifford and non-Clifford gates, wherein the number of non-Clifford gates is controlled by a tunable factor, wherein the tunable factor achieves a desired space-depth tradeoff for the quantum circuit and ancilla qubits used for at least one non-Clifford operation replace at least one Toffoli-gate.